Definition pr1_functor (A B : category) : (A × B) ⟶ A. Proof. apply (tpair _ (pr1_functor_data A B)). abstract (split; [ intro x; apply idpath | intros x y z f g; apply idpath ]). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat.