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Theorems · Definition · category theory

CategoryTheory.ShortComplex.rightHomology

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (S : CategoryTheory.ShortComplex C) → [S.HasRightHomology] → C

The right homology of a short complex, given by the H field of a chosen right homology data.

Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
66 results in Mathlib
Foundations
Depth 6 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasRightHomology

Around this declaration

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

CategoryTheory.ShortComplex.rightHomologyι · cited by 30ShortComplex.rightHomolog…CategoryTheory.ShortComplex.rightHomologyMap · cited by 27ShortComplex.rightHomolog…CategoryTheory.ShortComplex.rightHomologyIso · cited by 20ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso · cited by 14RightHomologyData.rightHo…CategoryTheory.ShortComplex.rightHomologyFunctor · cited by 7ShortComplex.rightHomolog…CategoryTheory.ShortComplex.opcyclesIsoRightHomology · cited by 6ShortComplex.opcyclesIsoR…CategoryTheory.ShortComplex.leftRightHomologyComparison · cited by 6ShortComplex.leftRightHom…CategoryTheory.ShortComplex.mapRightHomologyIso · cited by 5ShortComplex.mapRightHomo…CategoryTheory.ShortComplex.leftHomologyOpIso · cited by 4ShortComplex.leftHomology…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι · cited by 3RightHomologyData.rightHo…CategoryTheory.ShortComplex.rightHomologyOpIso · cited by 3ShortComplex.rightHomolog…CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary · cited by 3ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.homologyIso_rightHomologyData · cited by 3RightHomologyData.homolog…CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι · cited by 2ShortComplex.π_leftRightH…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι · cited by 2RightHomologyData.rightHo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.RightHomologyData.H · cited by 158RightHomologyData.HCategoryTheory.ShortComplex.HasRightHomology · cited by 125ShortComplex.HasRightHomo…CategoryTheory.ShortComplex.rightHomologyData · cited by 64ShortComplex.rightHomolog…ShortComplex.rightHomologyCITED BYCITES

Cites6

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Cited by80

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