Definition prod_nat_trans {C D₁ D₂ : category} {F G : C ⟶ category_binproduct D₁ D₂} (τ : F ∙ pr1_functor _ _ ⟹ G ∙ pr1_functor _ _) (θ : F ∙ pr2_functor _ _ ⟹ G ∙ pr2_functor _ _) : F ⟹ G. Proof. use make_nat_trans. - exact (λ x, τ x ,, θ x). - abstract (intros x y f ; use pathsdirprod ; [ apply (nat_trans_ax τ) | apply (nat_trans_ax θ) ]). 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.