Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology.congr_simp

∀ {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 hkf_1 : CategoryTheory.Limits.IsLimit kf),
  hkf = hkf_1 →
    ∀ (hcc hcc_1 : CategoryTheory.Limits.IsColimit cc),
      hcc = hcc_1 →
        ∀ {H : C} {π π_1 : kf.pt ⟶ H} (e_π : π = π_1) {ι ι_1 : H ⟶ cc.pt} (e_ι : ι = ι_1)
          (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.isoHomology S hkf hcc fac =
            CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology S hkf_1 hcc_1 ⋯

Defined in

Mathlib.Algebra.Homology.ShortComplex.Abelian

Cited by

0 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.EpiCategoryTheory.Mono