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 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 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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- "Abstract and Concrete Categories. The Joy of Cats". Jiri Adámek, Horst Herrlich, George E. Strecker.