fact: Definition make_abgr_isKernel_Criteria {X Y Z W : abgr_category} (f : X --> Y) (g : Y --> Z) (ZA : f · g = ZeroArrow (to_Zero abgr_Abelian) _ _) (H : ∏ (D : (∑ y : pr1 Y, pr1 g y = 1%multmonoid)), ∥ ∑ (x : abgrtogr X), monoidfuntobinopfun _ _ f x = (pr1 D) ∥) (isM : @isMonic abgr_category _ _ f) (h : abgr_Abelian ⟦W, Y⟧) (H' : h · g = ZeroArrow (to_Zero abgr_Abelian) W Z) : ∑ ψ : abgr_Abelian ⟦W, X⟧, ψ · f = h.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.Algebra.Groups UniMath.Algebra.Monoids UniMath.NumberSystems.Integers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian 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.BinDirectSums