Theorems · Theorem · category theory

CochainComplex.mappingCone.inr_f_descShortComplex_f

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  (S : CategoryTheory.ShortComplex (CochainComplex C ℤ)) (n : ℤ),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inr S.f).f n)
      ((CochainComplex.mappingCone.descShortComplex S).f n) =
    S.g.f n

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.ShortExact
Cited by: 3 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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 · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
HomologicalComplex.Xstatement · cited by 1,839
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CategoryTheory.ShortComplex.X₂statement · cited by 1,115
CochainComplexstatement and proof · cited by 1,016
CategoryTheory.ShortComplex.X₁statement · cited by 889
CategoryTheory.ShortComplex.X₃statement · cited by 876
HomologicalComplex.Hom.fstatement and proof · cited by 845

Cited by3

Results whose statement or proof uses this declaration.

CochainComplex.mappingCone.homologySequenceδ_trianglehproof · cited by 1
CochainComplex.mappingCone.inr_f_descShortComplex_f_assocproof · cited by 1
CochainComplex.mappingCone.map_descShortComplexproof · cited by 0