Definition benabou_cosmos_coends (V : benabou_cosmos) {C : category} (F : category_binproduct (C^opp) C ⟶ V) : coend_colimit F. Proof. use construction_of_coends. - apply benabou_cosmos_coequalizers. - apply benabou_cosmos_coproducts. - apply benabou_cosmos_coproducts. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.PosetCat. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.Coends. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed.