Automorphism group

Set

context $\bf C$ … concrete category
context $X:\mathrm{Ob}_{\bf C}$
definiendum $\mathrm{Aut}(X)\equiv\langle\!\langle X\cong X,\circ\rangle\!\rangle$

Elaboration

Obviously, $\circ$ denotes the concatentaion of arrows in $\bf C$ here.

Theorems

The automorphisms (which for concrete $\bf C$ can always be viewed as functions) equipped with $\circ$ indeed form a group.

Reference

Wikipedia: Automorphism


Context

Concrete category

Subset of

Group

Requirements

Automorphism