Definition iso_comma_pr2_preserves_bincoproduct (HC₁ : BinCoproducts C₁) (HC₂ : BinCoproducts C₂) : preserves_bincoproduct (iso_comma_pr2 F G). Proof. use preserves_bincoproduct_if_preserves_chosen. - apply bincoproducts_in_iso_comma. + exact HC₁. + exact HC₂. - intros x y. cbn. apply isBinCoproduct_BinCoproduct. 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.