Definition iso_comma_pr2_preserves_binproduct (HC₁ : BinProducts C₁) (HC₂ : BinProducts C₂) : preserves_binproduct (iso_comma_pr2 F G). Proof. use preserves_binproduct_if_preserves_chosen. - apply binproducts_in_iso_comma. + exact HC₁. + exact HC₂. - intros x y. cbn. apply isBinProduct_BinProduct. 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.