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