title: Amnestic functor
text: # 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 an isomorphism that covers the identity, but is not an identity morphism (its domain and codomain are not equal).
  
  