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 $\operatorname {id} \colon (X,d_{1})\to (X,d_{2})$ is a isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).

References

Look up amnestic in Wiktionary, the free dictionary.

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

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