Lemma isweq_hom_in_subcat_from_hom_in_precat (C : category) (C' : hsubtype (ob C)) (a b : ob (full_sub_precategory C')): isweq (hom_in_subcat_from_hom_in_precat _ _ a b). Proof. apply (isweq_iso _ (hom_in_precat_from_hom_in_full_subcat _ _ a b)). intro f. intros. apply idpath. intro f. destruct f. simpl. apply eq_in_sub_precategory. apply idpath. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.