Theorems · Theorem · category theory

CochainComplex.cm5b.i_f_comp

∀ {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),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.cm5b.i f).f n)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.fst.f n)
        ((CochainComplex.mappingCone.snd (CategoryTheory.CategoryStruct.id (CochainComplex.cm5b.I K))).v n n ⋯)) =
    CategoryTheory.Injective.ι (K.X n)

Defined in: Mathlib.Algebra.Homology.Factorizations.CM5b
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.EnoughInjectives

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
add_zerostatement and proof · cited by 2,707
HomologicalComplex.Xstatement and proof · cited by 1,839
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.Hom.fstatement · cited by 845
HomologicalComplex.dproof · cited by 598
CategoryTheory.Limits.biprodstatement · cited by 312

Cited by1

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CochainComplex.cm5b.i_f_comp_assocproof · cited by 0