Definition functor_precat_coproduct_cocone : @BinCoproduct [C, D] F G. Proof. use make_BinCoproduct. - apply BinCoproduct_of_functors. - apply coproduct_nat_trans_in1. - apply coproduct_nat_trans_in2. - use make_isBinCoproduct. + apply functor_category_has_homsets. + intros A f g. exists (tpair _ (coproduct_nat_trans A f g) (make_dirprod (coproduct_nat_trans_In1Commutes _ _ _ ) (coproduct_nat_trans_In2Commutes _ _ _ ))). apply coproduct_nat_trans_univ_prop. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.ProductCategory.