proposition: Lemma lim_endo_is_identity {g : graph} (D : diagram g C^op) (CC : LimCone D) (k : lim CC --> lim CC) (H : ∏ u, k · limOut CC u = limOut CC u) : identity _ = k.
proof: Proof. use (uniqueExists (limUnivProp CC _ _)). - now apply (limCone CC). - intros v; simpl. unfold compose. simpl. now apply id_left. - 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.Adjunctions.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.Graphs.Colimits