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Commit 3bcd0a36 authored by Philip Kaluđerčić's avatar Philip Kaluđerčić :u7121:
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Define full and faithful wrt. the morphism map of F

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...@@ -77,7 +77,7 @@ ...@@ -77,7 +77,7 @@
\begin{definition}\label{def:faithful}\label{def:full}\label{def:fullfaith}\label{def:functor-equivalence} \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 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 surjective, \emph{fully faithful}, if an \de{iso} is given between
every \de{object} in \(\Ob{\D}\) and \(\Ob{F(\C)}\), and every \de{object} in \(\Ob{\D}\) and \(\Ob{F(\C)}\), and
\emph{equivalence}, if all of the above hold. \emph{equivalence}, if all of the above hold.
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