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 Met_c→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 $\mathrm{id}:(X,d_1)\to (X,d_2)$ is an isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).

References

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

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