Definition (representation):
Let G {\displaystyle G} be a group and let C {\displaystyle {\mathcal {C}}} be a category. A representation of G {\displaystyle G} on an object A ∈ Obj ( C ) {\displaystyle A\in \operatorname {Obj} ({\mathcal {C}})} is a group homomorphism π : G → Aut ( C ) {\displaystyle \pi :G\to \operatorname {Aut} ({\mathcal {C}})} .
