fact: Definition precategory_object_in_subcat {C : category} {C':sub_precategories C} (a : ob C) (p : sub_precategory_predicate_objects C' a) : ob C' := tpair _ a p.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos