Definition pr2_preserves_bincoproduct {C₁ C₂ : category} (HC₁ : BinCoproducts C₁) (HC₂ : BinCoproducts C₂) : preserves_bincoproduct (pr2_functor C₁ C₂). Proof. use preserves_bincoproduct_if_preserves_chosen. - apply bincoproducts_in_product_category. + exact HC₁. + exact HC₂. - intros x y. 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.PrecategoryBinProduct. 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.