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Theorems · Definition · category theory

CochainComplex.HomComplex.CohomologyClass.mk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {K L : CochainComplex C ℤ} →
        {n : ℤ} → CochainComplex.HomComplex.Cocycle K L n → CochainComplex.HomComplex.CohomologyClass K L n

The cohomology class of a cocycle.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology
Cited by
34 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive

Around this declaration

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

CategoryTheory.InjectiveResolution.extMk · cited by 11InjectiveResolution.extMkCategoryTheory.ProjectiveResolution.extMk · cited by 11ProjectiveResolution.extMkCochainComplex.HomComplex.CohomologyClass.mk_surjective · cited by 7CohomologyClass.mk_surjec…CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk · cited by 4CohomologyClass.equiv_toS…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3ProjectiveResolution.extE…CochainComplex.HomComplex.CohomologyClass.mkAddMonoidHom · cited by 2CohomologyClass.mkAddMono…CochainComplex.HomComplex.CohomologyClass.mk_eq_zero_iff · cited by 2CohomologyClass.mk_eq_zer…CochainComplex.HomComplex.CohomologyClass.toHom_bijective · cited by 2CohomologyClass.toHom_bij…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk · cited by 1InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk · cited by 1ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1ProjectiveResolution.extE…CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKInjective · cited by 1CohomologyClass.bijective…CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjective · cited by 1CohomologyClass.bijective…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cocycle · cited by 130HomComplex.CocycleCochainComplex.HomComplex.CohomologyClass · cited by 49HomComplex.CohomologyClassQuotientAddGroup.leftRel · cited by 34QuotientAddGroup.leftRelCochainComplex.HomComplex.coboundaries · cited by 7HomComplex.coboundariesCohomologyClass.mkCITED BYCITES

Cites7

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Cited by37

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