diff --git a/Report/M2Diapo.tex b/Report/M2Diapo.tex index e3d6a63..b5a747b 100644 --- a/Report/M2Diapo.tex +++ b/Report/M2Diapo.tex @@ -106,7 +106,7 @@ \only<3>{\quad$\left(\Set^{\prod_{\Delta:X_\Con}X_\Ty(\Delta)}\right)$} \end{tabular} - \pause[3] + \pause[4] \[\begin{array}{rcl} H_1(\bullet) &=& 1_\Set \\ H_2(X_\Con) &=& X_\Con \\ @@ -247,6 +247,50 @@ \] \end{frame} + \begin{frame}{Adjunction $F \vdash G$} + + \end{frame} + + \begin{frame}{$FG \cong \Id$} + + \end{frame} + + \begin{frame}{Structure of the proof} + \begin{itemize} + \item $\CC_i$ + \item $\BB_i$ + \item $R_{i-1}^i : \BB_i \to \BB_{i-1}$ + $R_0^i : \BB_i \to \BB_0$ + \item $\tl^i : \BB_i \times \BB_0 \to \BB_i$ + $\inj_1^i : X \to X \tl^i Y$ + $\inj_2^i : Y \to R_0^i(X \tl^i Y)$ + \item $F_i : \BB_i \to \CC_i : G_i$ + \item $F_i \vdash G_i$ + \item $F_iG_i \cong \Id_{\CC_i}$ + $F_i\inj_1^i$ + \item $(R_{i-1}^i X) \tl^{i-1} Y \to R_{i-1}^i (X \tl^i Y)$ + \end{itemize} + \end{frame} + + \begin{frame}{Fibration of $\CC_i$} + + \end{frame} + + \begin{frame}{$S_i$ from syntax} + + \end{frame} + + \begin{frame}{Conclusion} + + \end{frame} + + \begin{frame}{Future work} + \begin{itemize} + \item Complete GAT + \item Proof Assistant Formalization + \item $S_i$ non-direct + \end{itemize} + \end{frame} \end{document}