proposition: Lemma is_pregroupoid_functor_cat {C : precategory} {D : category} (gr_D : is_pregroupoid D) : is_pregroupoid (functor_category C D).
proof: Proof. intros F G α; apply nat_trafo_z_iso_if_pointwise_z_iso. intros c; apply gr_D. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat