fact: Definition MonicsAreKernels (C : category) (D1 : Data1 C) (D2 : Data2 C D1) : UU := ∏ (x y : C) (M : Monic C x y), isKernel (pr1 D1) M (CokernelArrow (to_Cokernels D2 x y M)) (CokernelCompZero (to_Zero D1) (to_Cokernels D2 x y M)).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts 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.Opp UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive