Definition morphism_in_full_subcat {C : category} {C' : hsubtype (ob C)} {a b : ob (full_sub_precategory C')} (f : pr1 a --> pr1 b) : precategory_morphisms a b := precategory_morphisms_in_subcat 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.