proposition: Lemma opp_Kernel_isCokernel {y z : C} (f : (C^op)⟦y, z⟧) (Z : Zero (C^op)) (K : @Kernel (C^op) Z y z f) : isCokernel (opp_Zero Z) f (KernelArrow K) (opp_Kernel_eq f Z K).
proof: Proof. use make_isCokernel. - intros w h H'. rewrite <- opp_ZeroArrow in H'. use unique_exists. + exact (KernelIn Z K w h H'). + use (KernelCommutes Z K). + intros y0. apply hs. + cbn. intros y0 X. use (@KernelInsEq C^op). rewrite (KernelCommutes Z K). cbn. rewrite X. apply idpath. 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