Functors which reflect isomorphisms #

A functor F reflects isomorphisms if whenever f is an isomorphism, f was too.

It is formalized as a Prop valued typeclass ReflectsIsomorphisms F.

Any fully faithful functor reflects isomorphisms.

Define what it means for a functor F : C ⥤ D to reflect isomorphisms: for any morphism f : A ⟶ B, if f is an isomorphism then f is as well. Note that we do not assume or require that F is faithful.


    If F reflects isos and f is an iso, then f is an iso.