Proposition isaprop_preserves_locally_cartesian_closed {C₁ C₂ : category} {PB₁ : Pullbacks C₁} {PB₂ : Pullbacks C₂} {F : C₁ ⟶ C₂} (HF : preserves_pullback F) (H₁ : is_locally_cartesian_closed PB₁) (H₂ : is_locally_cartesian_closed PB₂) : isaprop (preserves_locally_cartesian_closed HF H₁ H₂). Proof. apply isaprop_preserves_dependent_products. Qed.
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.Limits.Preservation. Require Import UniMath.CategoryTheory.LocallyCartesianClosed.LocallyCartesianClosed. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. 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.CodFunctor. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodRightAdjoint. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts.