From 3bcd0a363f3d2f0915bd4345b3ec5bd7b7e75d8f Mon Sep 17 00:00:00 2001
From: Philip Kaludercic <philip.kaludercic@fau.de>
Date: Wed, 10 Apr 2024 16:09:17 +0200
Subject: [PATCH] Define full and faithful wrt. the morphism map of F
---
categories.tex | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/categories.tex b/categories.tex
index e7028b2..79d877b 100644
--- a/categories.tex
+++ b/categories.tex
@@ -77,7 +77,7 @@
\begin{definition}\label{def:faithful}\label{def:full}\label{def:fullfaith}\label{def:functor-equivalence}
A functor \(F : \map{\C}{\D}\) is called \emph{faithful}, if the
- object map \(F\) is injective, \emph{full}, if the \(F\) is
+ morphism map \(F\) is injective, \emph{full}, if the \(F\) is
surjective, \emph{fully faithful}, if an \de{iso} is given between
every \de{object} in \(\Ob{\D}\) and \(\Ob{F(\C)}\), and
\emph{equivalence}, if all of the above hold.
--
GitLab