Definition pstrans_pair_data {H : psfunctor B₁ B₂} (α : pstrans H F) (β : pstrans H G) : pstrans_data H binprod_psfunctor. Proof. use make_pstrans_data. - exact (λ x, ⟨ α x , β x ⟩). - intros x y f ; simpl. use make_invertible_2cell. + exact (precomp_prod_1cell _ _ _ _ • ⟪ lassociator _ _ _ • (prod_1cell_pr1 _ _ _ ▹ _) • psnaturality_of α f , lassociator _ _ _ • (prod_1cell_pr2 _ _ _ ▹ _) • psnaturality_of β f ⟫ • (precomp_prod_1cell_invertible _ _ _ _)^-1). + is_iso. * apply precomp_prod_1cell_invertible. * use binprod_ump_2cell_invertible. ** is_iso ; apply property_from_invertible_2cell. ** is_iso ; apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Constant. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations.