proposition: Lemma Cokernel_opp_isKernel {y z : C} (f : C⟦y, z⟧) (Z : Zero C) (CK : @Cokernel C Z y z f) : isKernel (Zero_opp Z) (CokernelArrow CK) f (Cokernel_opp_eq f Z CK).
proof: Proof. use make_isKernel. - intros w h H'. cbn in H'. use unique_exists. + rewrite <- ZeroArrow_opp in H'. exact (CokernelOut Z CK w h H'). + cbn. use CokernelCommutes. + intros y0. apply (has_homsets_opp hs). + cbn. intros y0 X. use CokernelOutsEq. rewrite CokernelCommutes. exact X. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts