From 455e92aacad7c14da5140e9136bd5ab1180d18a3 Mon Sep 17 00:00:00 2001
From: Philip Kaludercic <philip.kaludercic@fau.de>
Date: Wed, 10 Apr 2024 16:08:14 +0200
Subject: [PATCH] Mention the "respect system dynamics" phrase
---
coalgebra.tex | 11 ++++++-----
1 file changed, 6 insertions(+), 5 deletions(-)
diff --git a/coalgebra.tex b/coalgebra.tex
index 0f57783..a3abfde 100644
--- a/coalgebra.tex
+++ b/coalgebra.tex
@@ -10,11 +10,12 @@
\begin{definition}\label{def:fcoalgebra}
In a \de{category} \(\C\), given an \de{object} \(A \in \Ob{\C}\)
and an \de{endofunctor} \(F : \map{\C}{\C}\) the pair
- \(A, a : \map{A}{F(A)}\) is called a \emph{\fca}. A \fca-homomorphism
- \(f : \map{(A, a)}{(B, b)}\) ensures \( f \circ a = b \circ F(f)\).
- \fca{}s and \fca-homomorphisms constitute a separate \de{category}
- \(\Coalg{F}\) \refsk{fca-category}, which is \textbf{not} dual to
- \(\Alg{F}\), but to \(\Alg{\op{F}}\).
+ \(A, a : \map{A}{F(A)}\) is called a \emph{\fca}. A
+ \fca-homomorphism \(f : \map{(A, a)}{(B, b)}\) ensures
+ \( f \circ a = b \circ F(f)\). \fca{}s and \fca-homomorphisms
+ (which respect the system dynamics) constitute a separate
+ \de{category} \(\Coalg{F}\) \refsk{fca-category}, which is
+ \textbf{not} dual to \(\Alg{F}\), but to \(\Alg{\op{F}}\).
Despite that qualification, results like \cref{lem:lambek} or
\cref{def:initial-fa-construction} can mostly be derived analogously.
--
GitLab