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Amnestic functor

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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 is an identity.

An example of a functor which is not amnestic is the forgetful functor MetcTop 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).

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