Improve typesetting in the digraph example

background.tex

@@ -110,15 +110,16 @@
 
 \begin{example}\label{ex:gra}
   The \de{category} \(\Gra\) has
-  \href{https://en.wikipedia.org/wiki/Directed_graph}{digraphs}
+  \href{https://en.wikipedia.org/wiki/Directed_graph}{di(-rected )graphs}
   \((V, E)\) as \des{object} and
   \href{https://en.wikipedia.org/wiki/Graph_homomorphism}{graph
     homomorphisms} as \des{morphism}.  That means that a \de{morphism}
-  \(f : \map{X}{Y}\) have to preserve
+  \(f : \map{\mathfrak{A}}{\mathfrak{B}}\) have to preserve
   \href{https://en.wikipedia.org/wiki/Strongly_connected_component}{strongly
     connected components}, i.e.\
-  \[ \forall a, b \in V(X) \st a ~_{E(X)} b \implies f(a) ~_{E(Y)}
-    f(b).\]
+  \[ \forall a, b \in V(X) \st a \sim_{E(\mathfrak{A})} b \implies f(a)
+    \sim_{E(\mathfrak{B})} f(b),\] where \(x \sim_{E{\mathfrak{G}}} y\) says that
+  there is a path from \(x\) to \(y\) in the digraph \(\mathfrak{G}\).
 
   The \defn{initial}{initial object} are therefore the empty graph
   \(V = \{\}\), since there are no components to be preserved, and the