proposition: Lemma equiv_Kernel2_isEqualizer {a b : C} (f : C⟦a, b⟧) (K : Kernel f) : isKernel (equiv_Zero2 Z) (EqualizerArrow C K) f (equiv_Kernel2_eq f K).
proof: Proof. use (make_isKernel). intros w h H. use unique_exists. - use EqualizerIn. + exact h. + rewrite H. rewrite precomp_with_ZeroArrow. apply equiv_ZeroArrow. - use EqualizerArrowComm. - intros y. apply hs. - intros y T. cbn in T. use EqualizerInUnique. exact T. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Zero UniMath.CategoryTheory.Limits.Graphs.Equalizers UniMath.CategoryTheory.Limits.Kernels