Theorems · Theorem · category theory

CochainComplex.mappingCone.triangleRotateShortComplex_g

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {K L : CochainComplex C ℤ} (φ : K ⟶ L),
  (CochainComplex.mappingCone.triangleRotateShortComplex φ).g = (CochainComplex.mappingCone.triangle φ).rotate.mor₂

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit
Cited by: 0 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproducts

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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.Preadditivestatement and proof · cited by 3,309
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
CategoryTheory.ShortComplex.gstatement and proof · cited by 658
CategoryTheory.Pretriangulated.Triangle.obj₃statement · cited by 332
CategoryTheory.Pretriangulated.Triangle.obj₂statement · cited by 316
CategoryTheory.Pretriangulated.Triangle.mor₂statement · cited by 177
CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
CochainComplex.mappingCone.trianglestatement · cited by 48
CategoryTheory.Pretriangulated.Triangle.rotatestatement · cited by 43

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