Definition pair_nat_trans {C₁ C₂ C₁' C₂' : category} {F₁ F₂ : C₁ ⟶ C₁'} {G₁ G₂ : C₂ ⟶ C₂'} (τ : F₁ ⟹ F₂) (θ : G₁ ⟹ G₂) : pair_functor F₁ G₁ ⟹ pair_functor F₂ G₂. Proof. use make_nat_trans. - exact (λ x, τ (pr1 x) ,, θ (pr2 x)). - abstract (intros x y f ; cbn ; use pathsdirprod ; apply nat_trans_ax). 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.