## 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