In the mathematical field of category theory, an amnestic functor F : A â 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<sub>c</sub>âÂÂTop from the category of metric spaces with continuous functions for morphisms to the category of topological spaces. If and are equivalent metrics on a space then is an isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).