(Hepi : IsEpimorphism (m : morphism set_cat x y)) (Hmono : IsMonomorphism (m : morphism set_cat x y)) : @IsEquiv _ _ m (* NB: This depends on the (arguably accidental) fact that `ismono` and `isepi` from HoTT core are *definitionally* identical to the specialization of `IsMonomorphism` and `IsEpimorphism` to the category of sets.
Require Import Category.Core Functor.Core HomFunctor Category.Morphisms Category.Dual Functor.Dual Category.Prod Functor.Prod NaturalTransformation.Core SetCategory.Core Functor.Composition.Core. Require Import Basics.Trunc Types.Universe HIT.iso HoTT.Truncations.Core.