Definition precategory_binproduct_assoc_data (C0 C1 C2 : precategory_data) : functor_data (precategory_binproduct_data C0 (precategory_binproduct_data C1 C2)) (precategory_binproduct_data (precategory_binproduct_data C0 C1) C2). Proof. use tpair. - intros c. exact (tpair _ (tpair _ (pr1 c) (pr1 (pr2 c))) (pr2 (pr2 c))). - intros a b c. exact (tpair _ (tpair _ (pr1 c) (pr1 (pr2 c))) (pr2 (pr2 c))). 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.