Hom(GΓ,-) ---> H

This commit is contained in:
2024-07-20 00:52:38 +02:00
parent a4596781d3
commit f0c9453836
11 changed files with 55 additions and 34 deletions
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}\n\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":5,"label":{"kind":"normal","label":"R_0^{i-1} X_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":6,"label":{"kind":"normal","label":"f \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":7,"label":{"kind":"normal","label":"\\Cstr^{X'}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\Hom_{\\BB_{i-1}}(G_{i-1}O_i,X)","pos":[180,60],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^{i-1} X)_\\UU","pos":[450,60],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^{i-1} X')_\\UU","pos":[450,143],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\Hom_{\\BB_{i-1}}(G_{i-1}O_i,X')","pos":[180,143],"zindex":-10000}}],"sizeGrid":120,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}\n\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":5,"label":{"kind":"normal","label":"R_0^{i-1} X_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":6,"label":{"kind":"normal","label":"f \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":7,"label":{"kind":"normal","label":"\\Cstr^{X'}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"H_i(F_{i-1}X)","pos":[180,60],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^{i-1} X)_\\UU","pos":[450,60],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^{i-1} X')_\\UU","pos":[450,143],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"H_i(F_{i-1}X')","pos":[180,143],"zindex":-10000}}],"sizeGrid":120,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}\n\\newcommand{\\ensuremath}[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\\newcommand{\\inj}{\\operatorname{inj}}\n\\newcommand{\\idr}{\\operatorname{id}}\n","tabs":[{"active":true,"edges":[{"from":0,"id":10,"label":{"kind":"normal","label":"\\text{H3'}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":-1},"to":1},{"from":2,"id":11,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":12,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":13,"label":{"kind":"normal","label":"R_0^i(g \\oplus L_0^{i-1}\\Hbar_\\bullet(g,h))_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":14,"label":{"kind":"normal","label":"(R_0^i g \\oplus \\Hbar(g,h))_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":6,"id":15,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":16,"label":{"kind":"normal","label":"\\left[\\Hbar_\\bullet(g,h)\\right]_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":1,"id":17,"label":{"kind":"normal","label":"g \\circ \\dash","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":8},{"from":8,"id":18,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":0,"id":19,"label":{"kind":"normal","label":"(g \\oplus L_0^{i-1}\\Hbar_\\bullet(g,h)) \\circ \\dash","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":9},{"from":9,"id":20,"label":{"kind":"normal","label":"H3'","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":8},{"from":7,"id":21,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":1,"id":22,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X \\oplus L_0^{i-1}\\Hbar_\\bullet(X,Y))","pos":[306,72],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X)","pos":[570,72],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\left[\\Hbar_\\bullet(X,Y)\\right]_\\UU","pos":[722,72],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X \\oplus \\Hbar_\\bullet(X,Y)\\right]_\\UU","pos":[956,72],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"R_0^{i-1}(X \\oplus L_0^{i-1} \\Hbar_\\bullet(X,Y))_\\UU","pos":[1234,72],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"R_0^{i-1}(X' \\oplus L_0^{i-1} \\Hbar_\\bullet(X',Y'))_\\UU","pos":[1234,230],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X' \\oplus \\Hbar_\\bullet(X',Y')\\right]_\\UU","pos":[956,230],"zindex":-10000}},{"id":7,"label":{"isMath":true,"label":"\\left[\\Hbar_\\bullet(X',Y')\\right]_\\UU","pos":[722,230],"zindex":0}},{"id":8,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X')","pos":[570,230],"zindex":0}},{"id":9,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X' \\oplus L_0^{i-1}\\Hbar_\\bullet(X',Y'))","pos":[306,230],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}\n\\newcommand{\\ensuremath}[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\\newcommand{\\inj}{\\operatorname{inj}}\n\\newcommand{\\idr}{\\operatorname{id}}\n","tabs":[{"active":true,"edges":[{"from":0,"id":10,"label":{"kind":"normal","label":"\\text{H3'}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":-1},"to":1},{"from":2,"id":11,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":12,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":13,"label":{"kind":"normal","label":"R_0^i(g \\oplus L_0^{i-1}\\Hbar_\\bullet(g,h))_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":14,"label":{"kind":"normal","label":"(R_0^i g \\oplus \\Hbar_\\bullet(g,h))_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":6,"id":15,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":16,"label":{"kind":"normal","label":"\\left[\\Hbar_\\bullet(g,h)\\right]_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":1,"id":17,"label":{"kind":"normal","label":"g \\circ \\dash","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":8},{"from":8,"id":18,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":0,"id":19,"label":{"kind":"normal","label":"H_iF_{i-1}(g \\oplus L_0^{i-1}\\Hbar_\\bullet(g,h))","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":9},{"from":9,"id":20,"label":{"kind":"normal","label":"H3'","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":8},{"from":7,"id":21,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":1,"id":22,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"H_iF_{i-1}(X \\oplus L_0^{i-1}\\Hbar_\\bullet(X,Y))","pos":[306,72],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"H_iF_{i-1}(X)","pos":[530,72],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\left[\\Hbar_\\bullet(X,Y)\\right]_\\UU","pos":[682,72],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X \\oplus \\Hbar_\\bullet(X,Y)\\right]_\\UU","pos":[916,72],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"R_0^{i-1}(X \\oplus L_0^{i-1} \\Hbar_\\bullet(X,Y))_\\UU","pos":[1194,72],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"R_0^{i-1}(X' \\oplus L_0^{i-1} \\Hbar_\\bullet(X',Y'))_\\UU","pos":[1194,230],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X' \\oplus \\Hbar_\\bullet(X',Y')\\right]_\\UU","pos":[916,230],"zindex":-10000}},{"id":7,"label":{"isMath":true,"label":"\\left[\\Hbar_\\bullet(X',Y')\\right]_\\UU","pos":[682,230],"zindex":0}},{"id":8,"label":{"isMath":true,"label":"H_iF_{i-1}(X')","pos":[530,230],"zindex":0}},{"id":9,"label":{"isMath":true,"label":"H_iF_{i-1}(X' \\oplus L_0^{i-1}\\Hbar_\\bullet(X',Y'))","pos":[306,230],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":0,"id":5,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":6,"label":{"kind":"normal","label":"R_0^i(X)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":1,"id":7,"label":{"kind":"normal","label":"\\Cstr^X_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3}],"nodes":[{"id":0,"label":{"isMath":true,"label":"A","pos":[100,117.8125],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i X)","pos":[100,195.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"R_0^i(X)_\\El","pos":[358,117.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"R_0^i(X)_\\UU","pos":[358,195.8125],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":0,"id":5,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":6,"label":{"kind":"normal","label":"R_0^i(X)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":1,"id":7,"label":{"kind":"normal","label":"\\Cstr^X_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3}],"nodes":[{"id":0,"label":{"isMath":true,"label":"A","pos":[100,117.8125],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"H_iF_{i-1}(R_{i-1}^i X)","pos":[100,195.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"R_0^i(X)_\\El","pos":[358,117.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"R_0^i(X)_\\UU","pos":[358,195.8125],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":8,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":9,"label":{"kind":"normal","label":"R_0^i(X)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":10,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":11,"label":{"kind":"normal","label":"\\Cstr^X_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":4,"id":12,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":13,"label":{"kind":"normal","label":"R_0^i(X')_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":4,"id":14,"label":{"kind":"normal","label":"h'","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":7},{"from":7,"id":15,"label":{"kind":"normal","label":"\\Cstr^{X'}_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":0,"id":16,"label":{"kind":"normal","label":"!","style":{"alignment":"left","bend":0,"color":"black","dashed":true,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":1},"to":4},{"from":1,"id":17,"label":{"kind":"normal","label":"R_0^i(f)_\\El","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":18,"label":{"kind":"normal","label":"\\dash \\circ R_{i-1}^i f","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.10000000000000003,"tail":"none"},"zindex":0},"to":7},{"from":2,"id":19,"label":{"kind":"normal","label":"R_0^i(f)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.6,"tail":"none"},"zindex":0},"to":6},{"from":14,"id":20,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":12},{"from":10,"id":21,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":8}],"nodes":[{"id":0,"label":{"isMath":true,"label":"A","pos":[125,115],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"R_0^i(X)_\\El","pos":[403,115],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"R_0^i(X)_\\UU","pos":[403,297],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i X)","pos":[125,297],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"A'","pos":[249,190.8125],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"R_0^i(X')_\\El","pos":[521,190.8125],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"R_0^i(X')_\\UU","pos":[521,372.8125],"zindex":0}},{"id":7,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i X')","pos":[249,372.8125],"zindex":-10000}}],"sizeGrid":250,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":8,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":9,"label":{"kind":"normal","label":"R_0^i(X)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":10,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":11,"label":{"kind":"normal","label":"\\Cstr^X_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":4,"id":12,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":13,"label":{"kind":"normal","label":"R_0^i(X')_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":4,"id":14,"label":{"kind":"normal","label":"h'","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":7},{"from":7,"id":15,"label":{"kind":"normal","label":"\\Cstr^{X'}_i","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":0,"id":16,"label":{"kind":"normal","label":"!","style":{"alignment":"left","bend":0,"color":"black","dashed":true,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":1},"to":4},{"from":1,"id":17,"label":{"kind":"normal","label":"R_0^i(f)_\\El","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":18,"label":{"kind":"normal","label":"H_iF_{i-1}R_{i-1}^i f","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.10000000000000003,"tail":"none"},"zindex":0},"to":7},{"from":2,"id":19,"label":{"kind":"normal","label":"R_0^i(f)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.6,"tail":"none"},"zindex":0},"to":6},{"from":14,"id":20,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":12},{"from":10,"id":21,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":8}],"nodes":[{"id":0,"label":{"isMath":true,"label":"A","pos":[125,115],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"R_0^i(X)_\\El","pos":[403,115],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"R_0^i(X)_\\UU","pos":[403,297],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"H_iF_{i-1}(R_{i-1}^i X)","pos":[125,297],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"A'","pos":[249,190.8125],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"R_0^i(X')_\\El","pos":[521,190.8125],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"R_0^i(X')_\\UU","pos":[521,372.8125],"zindex":0}},{"id":7,"label":{"isMath":true,"label":"H_iF_{i-1}(R_{i-1}^i X')","pos":[249,372.8125],"zindex":-10000}}],"sizeGrid":250,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"(R_0^{i-1} (\\inj_1^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"\\inj_1^{i-1} \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":4,"id":9,"label":{"kind":"normal","label":"R_0^{i-1}(\\inj_1^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":3,"id":10,"label":{"kind":"normal","label":"(\\inj_1^{i-1} \\circ \\dash)^{-1}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.20000000000000004,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":11,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":0,"id":12,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":4,"id":13,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":3,"id":14,"label":{"kind":"normal","label":"\\Cstr^{X \\oplus L_0^i Y}","style":{"alignment":"left","bend":0.1,"color":"green","dashed":true,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i X)","pos":[220.5,73.5],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[951,73.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^{i-1} (R_{i-1}^i X \\oplus L_0^{i-1} Y))_\\UU","pos":[955.5,367.5],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i X \\oplus_{i-1} L_0^{i-1} Y)","pos":[220.5,367.5],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[718,301.8125],"zindex":-10000}},{"id":5,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i X)","pos":[448,300.8125],"zindex":-10000}}],"sizeGrid":147,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"(R_0^{i-1} (\\inj_1^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"H_iF_{i-1}\\inj_1^{i-1}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":4,"id":9,"label":{"kind":"normal","label":"R_0^{i-1}(\\inj_1^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":3,"id":10,"label":{"kind":"normal","label":"(\\inj_1^{i-1} \\circ \\dash)^{-1}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"normal","position":0.5,"tail":"none"},"zindex":-3},"to":5},{"from":5,"id":11,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":0,"id":12,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":4,"id":13,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":3,"id":14,"label":{"kind":"normal","label":"\\Cstr^{X \\oplus L_0^i Y}","style":{"alignment":"left","bend":0.1,"color":"green","dashed":true,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2}],"nodes":[{"id":0,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i X)","pos":[236.5,73.5],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[1013,73.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^{i-1} (R_{i-1}^i X \\oplus L_0^{i-1} Y))_\\UU","pos":[1017.5,249.5],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"H_iF_{i-1}(R_{i-1}^i X \\oplus_{i-1} L_0^{i-1} Y)","pos":[236.5,249.5],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[706,235.8125],"zindex":-10000}},{"id":5,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i X","pos":[556,234.8125],"zindex":-10000}}],"sizeGrid":147,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"(\\inj_1 \\circ \\dash)","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"\\{\\varphi_1 ; \\varphi_2\\} \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":2,"id":9,"label":{"kind":"normal","label":"(R_0^{i-1} \\inj_1^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"twoheads","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":10,"label":{"kind":"normal","label":"(R_0^i \\{\\varphi_1;\\varphi_2\\})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":11,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":1,"id":12,"label":{"kind":"normal","label":"R_{i-1}^i \\varphi_1 \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":2,"id":13,"label":{"kind":"normal","label":"(R_0^i \\varphi_1)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i X \\oplus L_0^{i-1} Y)","pos":[225,75],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i X)","pos":[525,75],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[681,241.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\Hom(G_{i-1}\\Gamma_i,R_{i-1}^i Z)","pos":[225,375],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"(R_0^{i-1} (R_{i-1}^i X \\oplus L_0^{i-1} Y))_\\UU","pos":[825,75],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[825,375],"zindex":0}}],"sizeGrid":150,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"H_iF_{i-1}\\inj^{i-1}_1","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"\\Cstr^X","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"H_iF_{i-1}\\{\\varphi_1 ; \\varphi_2\\}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":2,"id":9,"label":{"kind":"normal","label":"(R_0^{i-1} \\inj_1^{i-1})_\\UU","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.6,"tail":"none"},"zindex":-1},"to":4},{"from":4,"id":10,"label":{"kind":"normal","label":"(R_0^i \\{\\varphi_1;\\varphi_2\\})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":3,"id":11,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":1,"id":12,"label":{"kind":"normal","label":"R_{i-1}^i \\varphi_1 \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":2,"id":13,"label":{"kind":"normal","label":"(R_0^i \\varphi_1)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5}],"nodes":[{"id":0,"label":{"isMath":true,"label":"H_iF_{i-1}(R_{i-1}^i X \\oplus L_0^{i-1} Y)","pos":[225,75],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i X","pos":[477,75],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i X)_\\UU","pos":[571,142.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i Z","pos":[225,365],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"(R_0^{i-1} (R_{i-1}^i X \\oplus L_0^{i-1} Y))_\\UU","pos":[777,75],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[777,365],"zindex":0}}],"sizeGrid":150,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"(R_0^i Z)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":9,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":4,"id":10,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":11,"label":{"kind":"normal","label":"\\dash \\circ R_{i-1}^i f \\circ \\inj_1","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.10000000000000003,"tail":"hook"},"zindex":8},"to":3},{"from":4,"id":12,"label":{"kind":"normal","label":"\\left[R_{i-1}^i f \\circ \\inj_2\\right]_\\El","style":{"alignment":"left","bend":-0.2,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":4,"id":13,"label":{"kind":"normal","label":"\\phi_{XYZ}(f)_2","style":{"alignment":"left","bend":0,"color":"black","dashed":true,"head":"default","kind":"normal","position":0.6,"tail":"none"},"zindex":0},"to":0}],"nodes":[{"id":0,"label":{"isMath":true,"label":"E(z)","pos":[292,174],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^i Z)_\\El","pos":[492,174],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[492,304],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i Z)","pos":[292,304],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"A","pos":[100,100],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X)","pos":[101,224.8125],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"(R_0^i Z)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":8,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":9,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":4,"id":10,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":11,"label":{"kind":"normal","label":"H_iF_{i-1}(R_{i-1}^i f \\circ \\inj_1)","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.10000000000000003,"tail":"hook"},"zindex":8},"to":3},{"from":4,"id":12,"label":{"kind":"normal","label":"\\left[R_{i-1}^i f \\circ \\inj_2\\right]_\\El","style":{"alignment":"left","bend":-0.2,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":4,"id":13,"label":{"kind":"normal","label":"\\phi_{XYZ}(f)_2","style":{"alignment":"left","bend":0,"color":"black","dashed":true,"head":"default","kind":"normal","position":0.6,"tail":"none"},"zindex":0},"to":0}],"nodes":[{"id":0,"label":{"isMath":true,"label":"E(z)","pos":[290,174],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"(R_0^i Z)_\\El","pos":[490,174],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[490,304],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i Z","pos":[290,304],"zindex":-10000}},{"id":4,"label":{"isMath":true,"label":"A","pos":[100,100],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"H_iF_{i-1}X","pos":[101,224.8125],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"\\pi_1","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":8,"label":{"kind":"normal","label":"(R_0^i Z)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":1,"id":9,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":10,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":0,"id":11,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":12,"label":{"kind":"normal","label":"g \\circ \\dash","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":0,"id":13,"label":{"kind":"normal","label":"\\square_\\El","style":{"alignment":"left","bend":-0.2,"color":"blue","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":5,"id":14,"label":{"kind":"normal","label":"\\square_\\UU","style":{"alignment":"right","bend":0.10000000000000003,"color":"blue","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":9,"id":15,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":7}],"nodes":[{"id":0,"label":{"isMath":true,"label":"Y","pos":[130,130],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"E(Z)","pos":[390,130],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i Z)_\\El","pos":[608,130],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[608,234],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i Z)","pos":[390,234],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X)","pos":[130,234],"zindex":-10000}}],"sizeGrid":260,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand{\\coqproof}[1]{\\checkmark}","tabs":[{"active":true,"edges":[{"from":0,"id":6,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":7,"label":{"kind":"normal","label":"\\pi_1","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":8,"label":{"kind":"normal","label":"(R_0^i Z)_p","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":1,"id":9,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":10,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":0,"id":11,"label":{"kind":"normal","label":"h","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":5,"id":12,"label":{"kind":"normal","label":"H_iF_{i-1}g","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":0,"id":13,"label":{"kind":"normal","label":"\\square_\\El","style":{"alignment":"left","bend":-0.2,"color":"blue","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":5,"id":14,"label":{"kind":"normal","label":"\\square_\\UU","style":{"alignment":"right","bend":0.10000000000000003,"color":"blue","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":9,"id":15,"label":{"kind":"pullshout","label":"","style":{"alignment":"","bend":0,"color":"black","dashed":false,"head":"","kind":"normal","position":0,"tail":""},"zindex":0},"to":7}],"nodes":[{"id":0,"label":{"isMath":true,"label":"Y","pos":[130,130],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"E(Z)","pos":[390,130],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"(R_0^i Z)_\\El","pos":[608,130],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[608,234],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i Z","pos":[390,234],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"H_iF_{i-1}X","pos":[130,234],"zindex":-10000}}],"sizeGrid":260,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":8,"label":{"kind":"normal","label":"\\text{H3'}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":9,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":10,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":11,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":12,"label":{"kind":"normal","label":"R_0^{i-1}\\left\\{g;\\eta_0^i \\circ L_0^{i-1} \\square \\right\\}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":13,"label":{"kind":"normal","label":"(\\varepsilon_0^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":6,"id":14,"label":{"kind":"normal","label":"(R_0^{i-1} \\inj_2^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":6,"id":15,"label":{"kind":"normal","label":"R_0^{i-1}(\\eta_0^i \\circ L_0^{i-1} \\square)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.7,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":16,"label":{"kind":"normal","label":"\\square_\\UU \\circ \\Cstr^Z \\circ (g \\circ \\dash)","style":{"alignment":"right","bend":0.2,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":5},{"from":0,"id":17,"label":{"kind":"normal","label":"\\left\\{g;\\eta_0^i \\circ L_0^{i-1} \\square \\right\\} \\circ \\dash","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":7,"id":18,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":1,"id":19,"label":{"kind":"normal","label":"g \\circ \\dash","style":{"alignment":"left","bend":0,"color":"red","dashed":false,"head":"default","kind":"normal","position":0.4,"tail":"none"},"zindex":0},"to":7}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X \\oplus L_0^{i-1}\\Hbar(X,Y))","pos":[210,64],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,X)","pos":[329,129.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\Hbar(X,Y)_\\UU","pos":[410,64.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X \\oplus \\Hbar(X,Y)\\right]_\\UU","pos":[604.9999999999999,61.8125],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"R_0^{i-1}\\left(X \\oplus L_0^{i-1}\\Hbar(X,Y)\\right)","pos":[853,61.8125],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[853,303.8125],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"\\left[R_0^{i-1}L_0^{i-1}\\Hbar(X,Y)\\right]_\\UU","pos":[688,198.625],"zindex":0}},{"id":7,"label":{"isMath":true,"label":"\\Hom(G_{i-1}O_i,R_{i-1}^i Z)","pos":[210,306],"zindex":0}}],"sizeGrid":140,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":8,"label":{"kind":"normal","label":"\\text{H3'}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":9,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":10,"label":{"kind":"normal","label":"\\inj_2^0","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":11,"label":{"kind":"normal","label":"\\text{H1r}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":4,"id":12,"label":{"kind":"normal","label":"R_0^{i-1}\\left\\{g;\\eta_0^i \\circ L_0^{i-1} \\square \\right\\}","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":13,"label":{"kind":"normal","label":"(\\varepsilon_0^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":6},{"from":6,"id":14,"label":{"kind":"normal","label":"(R_0^{i-1} \\inj_2^{i-1})_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":4},{"from":6,"id":15,"label":{"kind":"normal","label":"R_0^{i-1}(\\eta_0^i \\circ L_0^{i-1} \\square)_\\UU","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.7,"tail":"none"},"zindex":0},"to":5},{"from":2,"id":16,"label":{"kind":"normal","label":"\\Cstr^Z \\circ H_iF_{i-1}g","style":{"alignment":"right","bend":0.2,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.30000000000000004,"tail":"none"},"zindex":0},"to":5},{"from":0,"id":17,"label":{"kind":"normal","label":"H_iF_{i-1}\\left\\{g;\\eta_0^i \\circ L_0^{i-1} \\square \\right\\}","style":{"alignment":"right","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":7,"id":18,"label":{"kind":"normal","label":"\\Cstr^Z","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":1,"id":19,"label":{"kind":"normal","label":"H_iF_{i-1}g","style":{"alignment":"left","bend":0,"color":"red","dashed":false,"head":"default","kind":"normal","position":0.4,"tail":"none"},"zindex":0},"to":7}],"nodes":[{"id":0,"label":{"isMath":true,"label":"H_iF_{i-1}(X \\oplus L_0^{i-1}\\Hbar_\\bullet(X,Y))","pos":[210,64],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"H_iF_{i-1}X","pos":[329,129.8125],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\Hbar(X,Y)_\\UU","pos":[410,64.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\left[R_0^{i-1} X \\oplus \\Hbar(X,Y)\\right]_\\UU","pos":[604.9999999999999,61.8125],"zindex":0}},{"id":4,"label":{"isMath":true,"label":"R_0^{i-1}\\left(X \\oplus L_0^{i-1}\\Hbar(X,Y)\\right)","pos":[853,61.8125],"zindex":0}},{"id":5,"label":{"isMath":true,"label":"(R_0^i Z)_\\UU","pos":[853,303.8125],"zindex":0}},{"id":6,"label":{"isMath":true,"label":"\\left[R_0^{i-1}L_0^{i-1}\\Hbar(X,Y)\\right]_\\UU","pos":[688,198.625],"zindex":0}},{"id":7,"label":{"isMath":true,"label":"H_iF_{i-1}R_{i-1}^i Z","pos":[210,306],"zindex":0}}],"sizeGrid":140,"title":"1"}]},"version":12}
+1 -1
View File
@@ -1 +1 @@
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":5,"label":{"kind":"normal","label":"G_{i-1} \\times \\id","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":6,"label":{"kind":"normal","label":"F_{i-1} \\times \\id","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":2,"id":7,"label":{"kind":"normal","label":"W","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":8,"label":{"kind":"normal","label":"E","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":9,"label":{"kind":"normal","label":"G_i","style":{"alignment":"right","bend":0.6,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":10,"label":{"kind":"normal","label":"F_i","style":{"alignment":"right","bend":-0.4,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":0},{"from":6,"id":11,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":8,"id":12,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":10,"id":13,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":9}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\CC_i","pos":[176,73.8125],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\left(X : \\CC_{i-1}\\right) \\times \\left.\\Set\\middle/\\Hom(O_i,X)\\right.","pos":[386,74],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\left(X : \\BB_{i-1}\\right) \\times \\left.\\Set\\middle/\\Hom(G_{i-1}\\Gamma_i,X)\\right.","pos":[386,171.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\BB_i","pos":[386,274],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}
{"graph":{"latexPreamble":"\\newcommand\\ensuremath[1]{#1}\n\\newcommand\\BB{{\\ensuremath{\\mathcal{B}}}}\n\\newcommand\\TT{{\\ensuremath{\\mathcal{T}}}}\n\\newcommand\\UU{{\\ensuremath{\\mathcal{U}}}}\n\\newcommand\\El{{\\ensuremath{\\operatorname{\\mathcal{E}l}}}}\n\\newcommand\\ii{{\\ensuremath{\\mathbf{i}}}}\n\\newcommand\\Cstr{{\\ensuremath{\\operatorname{\\mathcal{C}str}}}}\n\\newcommand\\Set{{\\ensuremath{\\operatorname{\\mathcal{S}et}}}}\n\\newcommand\\Hom{{\\ensuremath{\\operatorname{\\mathcal{H}om}}}}\n\\newcommand\\this{{\\ensuremath{\\operatorname{\\texttt{this}}}}}\n\\newcommand\\Hbar{{\\ensuremath{\\overline{H}}}}\n\\newcommand\\dash{{\\;\\textrm{---}\\;}}\n\n\\newcommand\\inj{\\operatorname{inj}}\n\\newcommand\\id{\\operatorname{id}}","tabs":[{"active":true,"edges":[{"from":0,"id":4,"label":{"kind":"normal","label":"","style":{"alignment":"left","bend":0,"color":"black","dashed":false,"head":"none","kind":"double","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":1,"id":5,"label":{"kind":"normal","label":"G_{i-1} \\times \\id","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":2,"id":6,"label":{"kind":"normal","label":"F_{i-1} \\times \\id","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":1},{"from":2,"id":7,"label":{"kind":"normal","label":"W","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":8,"label":{"kind":"normal","label":"E","style":{"alignment":"right","bend":0.30000000000000004,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":2},{"from":0,"id":9,"label":{"kind":"normal","label":"G_i","style":{"alignment":"right","bend":0.6,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":3},{"from":3,"id":10,"label":{"kind":"normal","label":"F_i","style":{"alignment":"right","bend":-0.4,"color":"black","dashed":false,"head":"default","kind":"normal","position":0.5,"tail":"none"},"zindex":0},"to":0},{"from":6,"id":11,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":5},{"from":8,"id":12,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":7},{"from":10,"id":13,"label":{"kind":"adjunction","label":"\\vdash","style":{"alignment":"over","bend":0,"color":"black","dashed":false,"head":"none","kind":"none","position":0.5,"tail":"none"},"zindex":0},"to":9}],"nodes":[{"id":0,"label":{"isMath":true,"label":"\\CC_i","pos":[176,73.8125],"zindex":0}},{"id":1,"label":{"isMath":true,"label":"\\left(X : \\CC_{i-1}\\right) \\times \\left.\\Set\\middle/H_iX\\right.","pos":[386,74],"zindex":0}},{"id":2,"label":{"isMath":true,"label":"\\left(X : \\BB_{i-1}\\right) \\times \\left.\\Set\\middle/H_iF_{i-1}X\\right.","pos":[386,171.8125],"zindex":0}},{"id":3,"label":{"isMath":true,"label":"\\BB_i","pos":[386,274],"zindex":0}}],"sizeGrid":200,"title":"1"}]},"version":12}