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