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

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