Definition left_whisker_data : pstrans_data (comp_psfunctor G F₁) (comp_psfunctor G F₂). Proof. use make_pstrans_data. - exact (λ X, #G (η X)). - intros X Y f ; cbn. use make_invertible_2cell. + exact ((psfunctor_comp G (η X) (#F₂ f)) • ##G (psnaturality_of η f) • (psfunctor_comp G (#F₁ f) (η Y))^-1). + is_iso. * apply psfunctor_comp. * apply psfunctor_is_iso. 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.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map1Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map2Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Identitor. Require Import UniMath.Bicategories.PseudoFunctors.Display.Compositor. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.Transformations.PseudoTransformation.