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Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.complex

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {Z : C} → CategoryTheory.ProjectiveResolution Z → ChainComplex C ℕ

the chain complex involved in the resolution

Defined in
Mathlib.CategoryTheory.Preadditive.Projective.Resolution
Cited by
82 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.ProjectiveResolution.π · cited by 50ProjectiveResolution.πCategoryTheory.ProjectiveResolution.cochainComplex · cited by 30ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.cochainComplexXIso · cited by 18ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.extMk · cited by 11ProjectiveResolution.extMkCategoryTheory.ProjectiveResolution.cochainComplex_d · cited by 8ProjectiveResolution.coch…CategoryTheory.ProjectiveResolution.isoLeftDerivedObj · cited by 8ProjectiveResolution.isoL…CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj · cited by 8ProjectiveResolution.isoL…CategoryTheory.ProjectiveResolution.Hom.hom · cited by 8Hom.homCategoryTheory.ProjectiveResolution.iso · cited by 7ProjectiveResolution.isoCategoryTheory.projectiveResolutions · cited by 7CategoryTheory.projective…CategoryTheory.ProjectiveResolution.lift · cited by 6ProjectiveResolution.liftCategoryTheory.ProjectiveResolution.fromLeftDerivedZero' · cited by 5ProjectiveResolution.from…CategoryTheory.ProjectiveResolution.homotopyEquiv · cited by 5ProjectiveResolution.homo…CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero · cited by 5ProjectiveResolution.lift…CategoryTheory.ProjectiveResolution.lift_commutes · cited by 5ProjectiveResolution.lift…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectChainComplex · cited by 350ChainComplexCategoryTheory.ProjectiveResolution · cited by 92CategoryTheory.Projective…ProjectiveResolution.complexCITED BYCITES

Cites5

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Cited by120

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