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Theorems · Definition · category theory

CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} →
        (h : S.RightHomologyData) → [inst_2 : S.HasRightHomology] → S.rightHomology ≅ h.H

The isomorphism S.rightHomology ≅ h.H induced by a right homology data h for a short complex S.

Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
14 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasRightHomology

Around this declaration

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

CategoryTheory.ShortComplex.RightHomologyData.homologyIso · cited by 27RightHomologyData.homolog…CategoryTheory.ShortComplex.mapRightHomologyIso · cited by 5ShortComplex.mapRightHomo…CategoryTheory.ShortComplex.rightHomologyOpIso · cited by 3ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyι · cited by 3RightHomologyData.rightHo…CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ι · cited by 2RightHomologyData.homolog…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ι · cited by 2RightHomologyData.rightHo…CategoryTheory.ShortComplex.RightHomologyData.homologyIso_inv_comp_homologyι · cited by 1RightHomologyData.homolog…CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eq · cited by 1RightHomologyMapData.righ…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_inv · cited by 1RightHomologyData.rightHo…CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv · cited by 1RightHomologyData.homolog…CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assoc · cited by 0RightHomologyData.homolog…CategoryTheory.ShortComplex.leftRightHomologyComparison_eq · cited by 0ShortComplex.leftRightHom…CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_comm · cited by 0RightHomologyMapData.righ…CategoryTheory.ShortComplex.RightHomologyData.mapRightHomologyIso_eq · cited by 0RightHomologyData.mapRigh…CategoryTheory.ShortComplex.rightHomologyIsoKernelDesc · cited by 0ShortComplex.rightHomolog…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.ShortComplex.RightHomologyData · cited by 211ShortComplex.RightHomolog…CategoryTheory.ShortComplex.RightHomologyData.H · cited by 158RightHomologyData.HCategoryTheory.ShortComplex.HasRightHomology · cited by 125ShortComplex.HasRightHomo…CategoryTheory.ShortComplex.rightHomology · cited by 66ShortComplex.rightHomologyCategoryTheory.ShortComplex.rightHomologyData · cited by 64ShortComplex.rightHomolog…CategoryTheory.ShortComplex.rightHomologyMapIso' · cited by 2ShortComplex.rightHomolog…RightHomologyData.rightHomolo…CITED BYCITES

Cites11

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Cited by18

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