Amnestic functor

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 Metc→Top from the category of metric spaces with continuous functions for morphisms to the category of topological spaces. If formula_1 and formula_2 are equivalent metrics on a space formula_3 then formula_4 is an isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).