fact: Definition PreAdditiveComps : UU := ∏ (x y : ob PA), (∏ (z : ob PA) (f : x --> y) (inf : pr1submonoid (@to_abgr PA x y) (PAS x y) f) (g : y --> z), pr1submonoid (@to_abgr PA x z) (PAS x z) (f · g)) × (∏ (z : ob PA) (f : x --> y) (g : y --> z) (ing : pr1submonoid (@to_abgr PA y z) (PAS y z) g), pr1submonoid (@to_abgr PA x z) (PAS x z) (f · g)).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels