\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Algebra::Aluffi
Endomorphisms and automorphisms
Endomorphism
An endomorphism is a morphism that [meets what criteria?].
For an object \( A \) in category \( \cat{C} \) the set of
endomorphisms of \( A \) are all morphisms in [what set?], which is
denoted as \( \mathrm{End_C}(A) \).
Automorphism
An automorphism is a morphism that [meets criteria 1] and [criterial 2].
For an object \( A \) in category \( \cat{C} \), the set of automorphisms for
\( A \) is denoted as \( \mathrm{Aut_C}(A) \). \( \mathrm{Aut_C}(A) \) is a
subset of [what set?].
