proposition: Lemma IsomMono {M : ExactCategory} {A A' B B':M} (f : A --> B) (f' : A' --> B') : IsoArrow f f' -> isAdmissibleMonomorphism f -> isAdmissibleMonomorphism f'.
proof: Proof. intros [g [h e]] i. apply (squash_to_hProp i); clear i; intros [C [p E]]. apply hinhpr. exists C. exists (z_iso_inv h · p). use (EC_IsomorphicToExact _ E). simple refine (make_MorphismPairIsomorphism (make_MorphismPair f p) (make_MorphismPair f' (z_iso_inv h · p)) g h (identity_z_iso C) e _). refine (assoc _ _ _ @ maponpaths (postcomp_with p) _ @ id_left p @ ! id_right p). apply z_iso_inv_after_z_iso. 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