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?].