diff --git a/background.tex b/background.tex index 3a88efc0ff70d6206f8b8e4fb87a219822e1fcb8..6daed4e6571ea0ce458295e8ca4b9ba2a1dd0242 100644 --- a/background.tex +++ b/background.tex @@ -118,8 +118,9 @@ \href{https://en.wikipedia.org/wiki/Strongly_connected_component}{strongly connected components}, i.e.\ \[ \forall a, b \in V(X) \st a \sim_{E(\mathfrak{A})} b \implies f(a) - \sim_{E(\mathfrak{B})} f(b),\] where \(x \sim_{E{\mathfrak{G}}} y\) says that - there is a path from \(x\) to \(y\) in the digraph \(\mathfrak{G}\). + \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 \(\mathfrak{G}\), + over the transitive-reflexive closure of edges. The \defn{initial}{initial object} are therefore the empty graph \(V = \{\}\), since there are no components to be preserved, and the