proposition: Lemma equiv_isEqualizer2 {a b : C} (f g : C⟦a, b⟧) (e : C) (h : C⟦e, a⟧) (H : h · f = h · g) : Limits.Equalizers.isEqualizer f g h H <- isEqualizer C f g e h H.
proof: Proof. intros X. set (E := make_Equalizer C f g e h H X). intros e' h' H'. use (unique_exists (EqualizerIn C E e' h' H')). - exact (EqualizerArrowComm C E e' h' H'). - intros y. apply hs. - intros y T. cbn in T. use (EqualizerInUnique 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.Isos UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Equalizers