Definition lift_functor_into_reindex_disp_nat_trans {C₁ C₂ C₃ : category} {D₁ : disp_cat C₁} {D₃ : disp_cat C₃} {F₁ F₁' : C₁ ⟶ C₂} {α : F₁ ⟹ F₁'} {F₂ : C₂ ⟶ C₃} {FF₁ : disp_functor (F₁ ∙ F₂) D₁ D₃} {FF₂ : disp_functor (F₁' ∙ F₂) D₁ D₃} (αα : disp_nat_trans (post_whisker α _) FF₁ FF₂) : disp_nat_trans α (lift_functor_into_reindex FF₁) (lift_functor_into_reindex FF₂). Proof. simple refine (_ ,, _). - exact (lift_functor_into_reindex_disp_nat_trans_data αα). - exact (lift_functor_into_reindex_disp_nat_trans_axioms αα). 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Section IsCartesianFromReindexDispCat. End IsCartesianFromReindexDispCat. Section IsOpCartesianFromReindexDispCat. End IsOpCartesianFromReindexDispCat.