Definition cartesian_to_is_pullback {C : comp_cat} {Γ₁ Γ₂ : C} {s : Γ₁ --> Γ₂} {A₁ : ty Γ₁} {A₂ : ty Γ₂} (t : A₁ -->[ s ] A₂) (Ht : is_cartesian t) : isPullback (comprehension_functor_mor_comm (comp_cat_comprehension C) t) := cartesian_isPullback_in_cod_disp _ (cartesian_disp_functor_on_cartesian (comp_cat_comprehension C) Ht).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat.