Rızacan

Exercises/Exercises.aux

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Exercises/Exercises.out

-\BOOKMARK [1][-]{section.1}{1. Week One}{}% 1

Exercises/Exercises.tex

@@ -28,7 +28,7 @@
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@@ -177,11 +177,11 @@
 %%--------------------------------------
 
 
-Welcome one and all to our shared exercise sheet. Questions, answers and comments will be posted the following way: 
+Welcome one and all to our shared exercise sheet. Questions, answers and comments will be posted the following way:
 
 \subsection{} What is the most creative color?\hfill \break
 
-\iam{Student} 
+\iam{Student}
 I don't know but it is not green.
 
 \iam{An Other Student}
@@ -193,7 +193,7 @@ Remember to sign you name using the \textbackslash  iam\{\}  command. Try to ans
 
 \section{Week One}
 
-\subsection{} The category \textbf{Rel} has as objects sets and morphisms $f:A\to B$ are \emph{relations}, that is subsets of the form $f\subseteq A\times B$. Composition in this category is given by 
+\subsection{} The category \textbf{Rel} has as objects sets and morphisms $f:A\to B$ are \emph{relations}, that is subsets of the form $f\subseteq A\times B$. Composition in this category is given by
 \begin{align*}
 g\circ f = \{ (a,c)\in A\times C \,|\, \exists b\in B \,\,\text{with}\,\, (a,b)\in f, (b,c)\in g\}
 \end{align*}
@@ -204,6 +204,9 @@ for $f\in A\times B$ and $g\in B\times C$. Show that \textbf{Rel} satisfies the
 \subsection{}  Check that functors compose in an associative way, proving that $\mathbf{Cat}$ is a category. \hfill \break
 
 \subsection{}  Prove that inverses are unique. \hfill \break
+\iam{Rızacan} Let $f$ be an arrow with Cod($f$)=$B$ and Dom($f$)=$A$. Suppose
+$g,g'$ are both inverses of $f$. Then by associativity $g'=\id_A\circ
+g'=(g\circ f)\circ g'= g\circ(f\circ g')=g\circ \id_B=g$.
 
 \subsection{} Argue whether the following \emph{isomorphisms} of categories hold:
 \begin{enumerate}

Exercises/Exercises.toc

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