fact: Definition restrict_functor_to_sub_precategory {C D : category} (C' : sub_precategories C) (F : functor C D) : functor C' D.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos