Definition iso_comma_pr1_preserves_pullback (HC₁ : Pullbacks C₁) (HC₂ : Pullbacks C₂) : preserves_pullback (iso_comma_pr1 F G). Proof. use preserves_pullback_if_preserves_chosen. - apply pullbacks_in_iso_comma. + exact HC₁. + exact HC₂. - intros x y z f g. cbn. apply isPullback_Pullback. 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation.