`{IsFull} `{IsFaithful} (H' : forall x y (m : morphism set_cat x y), IsEpimorphism m -> IsMonomorphism m -> IsIsomorphism m) : IsFullyFaithful. Proof. intros ? ?; hnf in * |- . apply H'; eauto. Qed.
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.