Theorems · Theorem · category theory

CochainComplex.mappingCone.map_id

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {K L : CochainComplex C ℤ} (φ : K ⟶ L),
  CochainComplex.mappingCone.map φ φ (CategoryTheory.CategoryStruct.id K) (CategoryTheory.CategoryStruct.id L) ⋯ =
    CategoryTheory.CategoryStruct.id (CochainComplex.mappingCone φ)

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated
Cited by: 0 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproducts

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Category.id_compproof · cited by 1,998
HomologicalComplex.Xstatement and proof · cited by 1,839
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.Hom.fproof · cited by 845
HomologicalComplex.HasHomotopyCofiberproof · cited by 225

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