proposition: Lemma equiv_isCoequalizer2 {a b : C} (f g : C⟦a, b⟧) (e : C) (h : C⟦b, e⟧) (H : f · h = g · h) : Limits.Coequalizers.isCoequalizer f g h H <- isCoequalizer C f g e h H.
proof: Proof. intros X. set (E := make_Coequalizer C f g e h H X). intros e' h' H'. use (unique_exists (CoequalizerOut C E e' h' H')). - exact (CoequalizerArrowComm C E e' h' H'). - intros y. apply C. - intros y T. cbn in T. use (CoequalizerOutUnique C E). exact T. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.Coequalizers