proposition: Lemma IdentityPlusMono {M : ExactCategory} {B C:M} (A:M) (f:B-->C) (AB : BinDirectSum A B) (AC : BinDirectSum A C) : isAdmissibleMonomorphism f -> isAdmissibleMonomorphism (directSumMap AB AC (identity A) f).
proof: Proof. intros i. use (IsomMono (directSumMap (reverseBinDirectSum AB) (reverseBinDirectSum AC) f (identity A)) (directSumMap AB AC (identity A) f)). - exists (SwitchIso _ _ _ _). exists (SwitchIso _ _ _ _). apply SwitchMapMapEqn. - apply MonoPlusIdentity. exact i. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Notations UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Subcategory.Full UniMath.MoreFoundations.Propositions