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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?].