Theorems · Theorem · category theory

CochainComplex.cm5b.i_f_comp_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.EnoughInjectives C] {K L : CochainComplex C ℤ} (f : K ⟶ L) (n : ℤ) {Z : C}
  (h : (CochainComplex.cm5b.I K).X n ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.cm5b.i f).f n)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.fst.f n)
        (CategoryTheory.CategoryStruct.comp
          ((CochainComplex.mappingCone.snd (CategoryTheory.CategoryStruct.id (CochainComplex.cm5b.I K))).v n n ⋯) h)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Injective.ι (K.X n)) h

Defined in

Mathlib.Algebra.Homology.Factorizations.CM5b

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.EnoughInjectives