Definition iso_comma_ump1_preserves_bincoproduct {C₀ : category} (H₁ : C₀ ⟶ C₁) (HH₁ : preserves_bincoproduct H₁) (H₂ : C₀ ⟶ C₂) (HH₂ : preserves_bincoproduct H₂) (α : nat_z_iso (H₁ ∙ F) (H₂ ∙ G)) : preserves_bincoproduct (iso_comma_ump1 F G H₁ H₂ α). Proof. intros x y z π₁ π₂ Hx. apply isBinCoproduct_in_iso_comma. - apply HH₁. exact Hx. - apply HH₂. exact Hx. 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.