Amnestic functor explained

In the mathematical field of category theory, an amnestic functor F : A → B is a functor for which an A-isomorphism ƒ is an identity whenever Fƒ is an identity.

An example of a functor which is not amnestic is the forgetful functor Met_c→Top from the category of metric spaces with continuous functions for morphisms to the category of topological spaces. If

d _{1} and d _{2} are equivalent metrics on a space X then \operatorname{id}\colon(X, d _{1)\to(X,} d _{2)} is an isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).

References

• "Abstract and Concrete Categories. The Joy of Cats". Jiri Adámek, Horst Herrlich, George E. Strecker.