proposition: Corollary ff_es_preserves_homsets (FFF : fully_faithful F) (FES : essentially_surjective F) (hsC : has_homsets C) : has_homsets D.
proof: Proof. refine (ff_es_homtype_property FFF FES (λ t, make_hProp _ (isapropisaset t)) _). apply hsC. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core