sAb: updated a picture

12 years ago · 35e2abd1fa
6 changed files with 101 additions and 89 deletions
--- a/thesis/3_SimplicialAbelianGroups.tex
+++ b/thesis/3_SimplicialAbelianGroups.tex
@ -39,12 +39,12 @@ This category $\DELTA$ will act as a protoype for these kind of geometric struct
 	(Or equivalently a covariant functor $X: \DELTA^{op} \to \Set.$)
 \end{definition}

-So the category of all simplicial sets, $\sSet$, is the functor category $\Set^{\DELTA^{op}}$, where morphisms are natural transformations. Because the face and degeneracy maps give all the maps in $\DELTA$ it is sufficient to define images of $\delta_i$ and $\sigma_i$ in order to define a functor $X: \DELTA^{op} \to \Set$. And hence we can picture a simplicial set as done in figure~\ref{fig:simplicial_abelian_group}. Comparing this to figure~\ref{fig:delta_cat} we see that the arrows are reversed, because $X$ is a contravariant functor.
+So the category of all simplicial sets, $\sSet$, is the functor category $\Set^{\DELTA^{op}}$, where morphisms are natural transformations. Because the face and degeneracy maps give all the maps in $\DELTA$ it is sufficient to define images of $\delta_i$ and $\sigma_i$ in order to define a functor $X: \DELTA^{op} \to \Set$. And hence we can picture a simplicial set as done in figure~\ref{fig:simplicial_set}. Comparing this to figure~\ref{fig:delta_cat} we see that the arrows are reversed, because $X$ is a contravariant functor.

 \begin{figure}
-	\includegraphics{simplicial_abelian_group}
-	\caption{A simplicial abelian group.}
-	\label{fig:simplicial_abelian_group}
+	\includegraphics{simplicial_set}
+	\caption{A simplicial set.}
+	\label{fig:simplicial_set}
 \end{figure}


--- a/thesis/images/delta_cat.pdf
+++ b/thesis/images/delta_cat.pdf
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+++ b/thesis/images/delta_cat.svg
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--- a/thesis/images/simplicial_abelian_group.pdf
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--- a/thesis/images/simplicial_set.pdf
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