diff --git a/Report/M2Diapo.tex b/Report/M2Diapo.tex
index c598b0c..7902700 100644
--- a/Report/M2Diapo.tex
+++ b/Report/M2Diapo.tex
@@ -336,6 +336,7 @@
 	\end{frame}
 	
 	\begin{frame}{Constructing $G_3$}
+		\vspace{-2ex}
 		\begin{columns}
 			\begin{column}{.5\textwidth}
 		\begin{center}
@@ -356,30 +357,41 @@
 		\end{array}\]
 		}
 		\pause
-		\[\begin{array}{ccccccc}
+		\renewcommand{\arraystretch}{0.5}
+		\[\begin{array}{ccccccccc}
 			X_\UU & = &
 			\{\star\} & \uplus &
 			Y_\Con & \uplus&
-			\displaystyle\coprod_{\Delta \in Y_\Con}Y_\Ty(\Delta) \\
-			X_\El(\inj_1(\star)) & = &
-			Y_\Con &&&&\\
-			X_\El(\inj_2(\Gamma)) & = &
-			&&Y_\Ty(\Gamma) &&\\
-			X_\El(\inj_3(\Delta,A)) & = &
-			&&&& Y_\Tm(\Delta,A)\\
+			\displaystyle\coprod_{\Delta \in Y_\Con}Y_\Ty(\Delta) &
+			\xrightarrow{X_\El}&\Set\\
+			\pause
+			&& \tikzmark{1}{\star} &&&&&&\tikzmark{2}{Y_\Con}\\
+			X_\El & &
+			&&\tikzmark{3}{\Gamma}&&&&\tikzmark{4}{Y_\Ty(\Gamma)}\\
+			&&&&&& \tikzmark{5}{(\Delta,A)}&& \tikzmark{6}{Y_\Tm(\Delta,A)}\\
 			
 		\end{array}\]
+		\begin{tikzpicture}[overlay,remember picture]
+			\draw[|->] (1) to (2);
+			\draw[|->] (3) to (4);
+			\draw[|->] (5) to (6);
+		\end{tikzpicture}
 		\pause
+		\begin{columns}
+		\begin{column}{.5\textwidth}
 		\[\begin{array}{lcl}
-			\XCon_X &=& \inj_1(\star)\\
-			\XTy_X(\Gamma) &=& \inj_2(\Gamma) \\
-			\XTm_X(\Delta,A) &=& \inj_3(\Delta,A)
+			\XCon_X &=& \star \in \{\star\}\\
+			\XTy_X(\Gamma) &=& \Gamma \in Y_\Con \\
+			\XTm_X(\Delta,A) &=& (\Delta,A) \in \displaystyle\coprod_{\Delta \in Y_\Con}Y_\Ty(\Delta)
 		\end{array}\]
+		\end{column}
 		\pause
-		\vspace{-1.5ex}
+		\begin{column}{.5\textwidth}
 		\begin{tcolorbox}
 			All sorts of $X_\UU$ are in the image of some constructor $(\XCon_X,\XTy_X,\XTm_X)$
 		\end{tcolorbox}
+		\end{column}
+		\end{columns}
 	\end{frame}
 	
 	\begin{frame}{Constructing $F_3$}
@@ -405,7 +417,7 @@
 		\pause[5]
 		\vspace{-.5ex}
 		\begin{tcolorbox}
-			Each object of $Y$ are associated by $X_\El$ to some constructor
+			The preimage by $X_\El$ of each object of $Y$ is a sort of $X_\UU$ constructed by some constructor
 		\end{tcolorbox}
 		
 	\end{frame}
@@ -417,13 +429,18 @@
 		\pause
 		
 		\begin{remark}
-			All sorts of $G_3Y$ are reached by some constructor of $G_3Y$
+			Morphisms of $\BB_3$ and $\CC_3$ both respect constructors
+			\pause
 			
-			\uncover<3>{\ding{220}$\Hom_{\BB_3}\left(G_3Y,X\right)$ transforms constructible into constructible}
+			All sorts of $G_3Y_\UU$ are in the image of some constructor $(\XCon_{G_3Y},\XTy_{G_3Y},\XTm_{G_3Y})$
 			
-			Each object of $F_3X$ are associated by $X_\El$ to some constructor of $X$
+			\ding{220}$\Hom_{\BB_3}\left(G_3Y,X\right)$ morphisms are only defined on constructors
 			
-			\uncover<3>{\ding{220}$\Hom_{\CC_3}\left(Y,F_3X\right)$ transforms constructible into constructible}
+			\pause
+			
+			The preimage by $X_\El$ of each object of $F_3X$ is a sort of $X_\UU$ constructed by some constructor
+			
+			\ding{220}$\Hom_{\CC_3}\left(Y,F_3X\right)$ morphisms only send to constructible terms
 		\end{remark}
 	\end{frame}
 	
@@ -431,7 +448,7 @@
 	
 	\begin{frame}{Conclusion}
 		\begin{center}
-			\hspace{2ex}$\CC$ \hspace{3.5cm} $\BB$
+			\hspace{9.2ex}$\CC$ \hspace{3.7cm} $\BB$
 			\vspace{.5cm}
 			
 			\includesvg[scale=.4]{graphs/diagrammeFG.svg}
@@ -510,3 +527,4 @@
 
 
 
+
diff --git a/Report/headerDiapo.tex b/Report/headerDiapo.tex
index 9072d22..379ca1b 100644
--- a/Report/headerDiapo.tex
+++ b/Report/headerDiapo.tex
@@ -191,3 +191,9 @@
 		\tableofcontents[currentsection,hideothersubsections,sections=\value{section}]
 	\end{frame}
 }
+
+\newcommand{\tikzmark}[2]{\tikz[remember picture] \node (#1) {$#2$};}
+\makeatletter
+\newcommand{\mathleft}{\@fleqntrue\@mathmargin0pt}
+\newcommand{\mathcenter}{\@fleqnfalse}
+\makeatother