« Category Theory

Definition. Isomorphism in a Category [005W]

An isomorphism is a morphism for which there exists a morphism such that and . In that case we say that and are isomorophic , in symbols .

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Definition. Automorphism [0069]

An endomorphism that is also an isomorphism is called an an automorphism.

Lemma. Inverse isomorphisms are unique [006B]

the left inverse and right inverse to a common morphism coincide. This means every morphism can have at most one inverse isomorphism.

Proof. TODO