proposition: Lemma colim_endo_is_identity {C : precategory} {g : graph} (D : diagram g C) (CC : ColimCocone D) (k : colim CC --> colim CC) (H : ∏ u, colimIn CC u · k = colimIn CC u) : identity _ = k.
proof: Proof. use (uniqueExists (colimUnivProp CC _ _)). - now apply (colimCocone CC). - intros v; simpl. now apply id_right. - simpl; now apply H. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core