diff --git a/ACV 2026/slides.tex b/ACV 2026/slides.tex
index 3057f6c..50d3f02 100644
--- a/ACV 2026/slides.tex	
+++ b/ACV 2026/slides.tex	
@@ -165,7 +165,7 @@
 	The content of the talk:
 	\begin{itemize}
 		\item Intuitive introduction to coalgebra and (bi)simulation
-		\item Reviewing basic definitions of coalgebra and (bi)simulation
+		\item Reviewing definitions of coalgebra and (bi)simulation
 		\item Our motivation: To ease proving program equivalence
 		\item Relator-based notions
 		\item Span-based notions
@@ -177,14 +177,14 @@
 		When can we say that two systems \emph{behave the same}?
 	\end{alertblock}
 	\vspace{-0.4cm}
-	This question is everywhere, often silently assumed:\vspace{-0.4cm}
+	This question is everywhere, for example:\vspace{-0.4cm}
 	\begin{itemize}
 		\setlength{\itemsep}{6pt}
-		\item[\faServer] \textbf{Hardware redesign.} A chip redesigned for cheaper production must still compute exactly what the old one did.
+		\item[\faServer] \textbf{Hardware redesign.} A chip redesigned for a cheaper price must still compute exactly what the old one did.
 		\item[\faCode] \textbf{Software upgrades.} A bank replaces its backend --- from the customer's view (balances, transactions), nothing should change.
 	\end{itemize}
 	\vspace{0.2cm}
-	\begin{block}{The catch}
+	\begin{block}{The point}
 		``Behaving the same'' is intuitive, but making it \emph{precise} and \emph{checkable} is surprisingly subtle.
 	\end{block}
 \end{frame}
@@ -453,8 +453,8 @@
 	-The method, applies a closure on the bisimilarity relation on $T$.\\
 	-Then one should prove that the result is a simulation.\\
 	-The closure preserves symmetry, and symmetric simulation is a bisimulation in traditional definitions.\\
-	-We have found out that it is not always the case.\\
-	-That is why we want to know when exactly a symmetric simulation is a bisimulation.
+	-We need to know how to generally derive bisimulation from simulation.\\
+	-And what is the impact of choosing specific notion of simulation (span-based, relation-based)?
 \end{frame}
 
 \begin{frame}{Relators and Simulations}
@@ -465,7 +465,7 @@
 		
 		%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 		\column{.47\textwidth}
-		To define coalgebraic simulation, relators are invented.
+		Relators unify simulation and bisimulation.
 		\begin{alertblock}{Relator}
 		Assuming $F:\Set\to\Set$ is a functor, an $F$-relator a monotone map that sends a morphism of $\rel$ that is a relation $X\rto Y$ to a relation $FX\rto FY$. 
 		\end{alertblock}
@@ -533,7 +533,7 @@
 				\begin{alertblock}{Symmetrization of a Relator}
 						Symmetrization of a relator $\relar$ is defined as:
 						\begin{gather*}
-								\hat{\relar}=\relar r\cap (\relar r^{-1})^{-1}
+								\hat{\relar}r=\relar r\cap (\relar r^{-1})^{-1}
 							\end{gather*}
 				\end{alertblock}
 						\begin{block}{Symmetric Relators}
@@ -658,8 +658,8 @@
 	\vspace{-0.1cm}
 	\begin{block}{}
 		\begin{itemize}
-		\item Although, not every sound and complete relator is a Barr relator.\\
-		\item We do not know when the symmetrizaion of a Barr relator is a Barr relator.
+		\item Although, not every sound and complete relator is a Barr relator!\\
+		\item We do not know when Clause 3 does not produce a Barr relator.
 	\end{itemize}
 	\end{block}
 \end{frame}