Definition precategory_morphisms_in_subcat {C : category} {C':sub_precategories C} {a b : ob C'}(f : pr1 a --> pr1 b) (p : sub_precategory_predicate_morphisms C' (pr1 a) (pr1 b) (f)) : precategory_morphisms (C:=C') a b := tpair _ f p.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos.