proposition: Lemma SumOfAdmissibleEpis {M:ExactCategory} {A B A' B':M} (AA' : BinDirectSum A A') (BB' : BinDirectSum B B') (f : A --> B) (f' : A' --> B') : isAdmissibleEpimorphism f -> isAdmissibleEpimorphism f' -> isAdmissibleEpimorphism (directSumMap AA' BB' f f').
proof: Proof. intros e e'. apply (squash_to_hProp e); clear e; intros [C [g e]]. apply (squash_to_hProp e'); clear e'; intros [C' [g' e']]. apply (squash_to_hProp (to_hasBinDirectSums C C')); intros CC'. exact (ExactToAdmEpi (SumOfExactSequences CC' _ _ e e')). Qed.
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