Amnestic functor

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