From ee1ea57fd8d9b85609071fad9f9e59c00a22aab0 Mon Sep 17 00:00:00 2001
From: Philip Kaludercic <philip.kaludercic@fau.de>
Date: Fri, 22 Mar 2024 14:37:18 +0100
Subject: [PATCH] Rephrase colimit definition

---
 constructions.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/constructions.tex b/constructions.tex
index b8ce21a..89b4db9 100644
--- a/constructions.tex
+++ b/constructions.tex
@@ -73,10 +73,10 @@
 \end{definition}
 
 \begin{definition}\label{def:colimit}\label{def:cocone}
-  A \emph{colimit} is a \emph{cocone}
+  A \emph{colimit}
   \(\left(K, \left(\inm{j} : \map{F(j)}{K}\right)_{j \in
-      \Ob{\J}}\right)\) is \de{dual} to a
-  \de{limit}, ensuring
+      \Ob{\J}}\right)\) is a \emph{cocone}, \de{dual} to a
+  \de{limit}, and ensures
   \[ \forall j \in \Ob{\J} \forall C \exists! h : \map{K}{C} \st h \circ \inm{j} = f_j. \]
 \end{definition}
 
-- 
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