Definition hom_in_subcat_from_hom_in_precat (C : category) (C' : hsubtype (ob C)) (a b : ob (full_sub_precategory C')) (f : pr1 a --> pr1 b) : a --> b := tpair _ f tt.
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.