Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  (S : CategoryTheory.ShortComplex C) {kf : CategoryTheory.Limits.KernelFork S.g}
  {cc : CategoryTheory.Limits.CokernelCofork S.f} (hkf : CategoryTheory.Limits.IsLimit kf)
  (hcc : CategoryTheory.Limits.IsColimit cc) {H : C} {π : kf.pt ⟶ H} {ι : H ⟶ cc.pt}
  (fac :
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Fork.ι kf) (CategoryTheory.Limits.Cofork.π cc) =
      CategoryTheory.CategoryStruct.comp π ι)
  [inst_2 : CategoryTheory.Epi π] [inst_3 : CategoryTheory.Mono ι],
  (CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation S hkf hcc fac).left =
    CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData S hkf hcc fac

Defined in

Mathlib.Algebra.Homology.ShortComplex.Abelian

Cited by

0 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.EpiCategoryTheory.Mono