fact: Definition precategory_object_from_sub_precategory_object (C:category) (C':sub_precategories C) (a : sub_ob C') : ob C := pr1 a.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos