| context | $\bf C$ … concrete category |
| context | $X:\mathrm{Ob}_{\bf C}$ |
| definiendum | $\mathrm{Aut}(X)\equiv\langle\!\langle X\cong X,\circ\rangle\!\rangle$ |
Obviously, $\circ$ denotes the concatentaion of arrows in $\bf C$ here.
The automorphisms (which for concrete $\bf C$ can always be viewed as functions) equipped with $\circ$ indeed form a group.
Wikipedia: Automorphism