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Theorems · Definition · category theory

HomotopyCategory.spectralObjectMappingCone

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        [inst_3 : CategoryTheory.Limits.HasBinaryBiproducts C] →
          CategoryTheory.Triangulated.SpectralObject (HomotopyCategory C (ComplexShape.up ℤ)) (CochainComplex C ℤ)

The spectral object with values in (HomotopyCategory C (.up ℤ) that is indexed by CochainComplex C ℤ.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.SpectralObject
Cited by
2 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasBinaryBiproducts
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Around this declaration

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HomotopyCategory.spectralObjectMappingCone_δ'_app · cited by 0HomotopyCategory.spectral…HomotopyCategory.spectralObjectMappingCone_ω₁ · cited by 0HomotopyCategory.spectral…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCategoryTheory.ComposableArrows · cited by 627CategoryTheory.Composable…CategoryTheory.Pretriangulated.Triangle.mor₃ · cited by 178Triangle.mor₃CategoryTheory.Limits.HasBinaryBiproducts · cited by 165Limits.HasBinaryBiproductsCategoryTheory.ComposableArrows.map' · cited by 133ComposableArrows.map'HomotopyCategory · cited by 132HomotopyCategoryHomotopyCategory.quotient · cited by 109HomotopyCategory.quotientCategoryTheory.Functor.mapTriangle · cited by 87Functor.mapTriangleHomotopyCategory.spectralObje…CITED BYCITES

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