Definition pre_whisker_disp_nat_trans {C₁ C₂ C₃ : category} {F : C₁ ⟶ C₂} {G₁ G₂ : C₂ ⟶ C₃} {n : G₁ ⟹ G₂} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} {D₃ : disp_cat C₃} (FF : disp_functor F D₁ D₂) {GG₁ : disp_functor G₁ D₂ D₃} {GG₂ : disp_functor G₂ D₂ D₃} (nn : disp_nat_trans n GG₁ GG₂) : disp_nat_trans (pre_whisker F n) (disp_functor_composite FF GG₁) (disp_functor_composite FF GG₂). Proof. use tpair. - exact (λ x xx, nn (F x) (FF x xx)). - abstract (intros x y f xx yy ff ; cbn ; rewrite (disp_nat_trans_ax nn) ; apply maponpaths_2 ; apply C₃). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.