Proposition cod_right_beck_chevalley {w x y z : C} (f : x --> w) (g : y --> w) (h : z --> y) (k : z --> x) (p : k · f = h · g) (H : isPullback p) : right_beck_chevalley HD f g h k p (HC x w f) (HC z y h). Proof. use right_from_left_beck_chevalley. - apply is_right_adjoint_cod_fiber_functor. - apply is_right_adjoint_cod_fiber_functor. - use cod_left_beck_chevalley. apply is_symmetric_isPullback. exact H. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.LocallyCartesianClosed.LocallyCartesianClosed. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DualBeckChevalley.