proposition: Lemma KernelEndo_is_identity {y z : C} {g : y --> z} {K : Kernel g} (φ : C⟦K, K⟧) (H : φ · (KernelArrow K) = KernelArrow K) : identity K = φ.
proof: Proof. set (H1 := tpair ((fun φ' : C⟦K, K⟧ => φ' · _ = _)) φ H). assert (H2 : identity_is_KernelIn K = H1). - apply proofirrelevancecontr. apply (KernelisKernel K). apply KernelCompZero. - apply (base_paths _ _ H2). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Zero