Automorphism

An automorphism is an endomorphism that is isomorphic.

Definition

Definition Automorphism Let $𝒞︀$ be a category. An automorphism on $𝑋 : 𝒞︀$ is an endomorphism $𝑓 : 𝑋 \to 𝑋$ that is an isomorphism.

Let us note $Aut (𝑋)$ the set of automorphisms, which happens to be a group.

We will show that $Aut$ lifts to a 1-functor from the groupoid previewcore of $𝒞︀$

Aut : core (𝒞︀) \to 𝐆𝐫𝐩