From c649851b39ed0c2f2f074f6f12f49cdacfe90478 Mon Sep 17 00:00:00 2001 From: Philip Kaludercic <philip.kaludercic@fau.de> Date: Fri, 22 Mar 2024 14:22:49 +0100 Subject: [PATCH] Define functor category when defining functor categories, not `Cat' --- background.tex | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/background.tex b/background.tex index 9550b00..93b720c 100644 --- a/background.tex +++ b/background.tex @@ -89,9 +89,11 @@ \end{example} \begin{example}\label{ex:cat} - The \de{category} of functors \(\fc{\C}{\D}\) - has \defn{category}{categories} as \des{object} and \des{functor} as - \des{morphism}, given that \(\C\) is \de{small}. + Given the \defn{category}{categories} \(\C\) (\de{small}) and + \(\D\), the \emph{functor category} \(\fc{\C}{\D}\) has + \des{functor} \(F : \map{\C}{\D}\) as \des{object} and + \defn{nattran}{natural transformations} \(\eta : \map{F}{G}\) as + \des{morphism}. \end{example} \begin{example}\label{ex:veck} -- GitLab