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Theorems · Definition · category theory

CochainComplex.HomComplex.CohomologyClass

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] → CochainComplex C ℤ → CochainComplex C ℤ → ℤ → Type v

The type of cohomology classes of degree n in the complex of morphisms from K to L.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology
Cited by
49 results in Mathlib
Foundations
Depth 68 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.

CochainComplex.HomComplex.CohomologyClass.mk · cited by 34CohomologyClass.mkCategoryTheory.ProjectiveResolution.extEquivCohomologyClass · cited by 19ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extEquivCohomologyClass · cited by 19InjectiveResolution.extEq…CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom · cited by 10CohomologyClass.toSmallSh…CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass · cited by 9ProjectiveResolution.extA…CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass · cited by 9InjectiveResolution.extAd…CochainComplex.HomComplex.CohomologyClass.mk_surjective · cited by 7CohomologyClass.mk_surjec…CochainComplex.HomComplex.CohomologyClass.toHom · cited by 6CohomologyClass.toHomCochainComplex.HomComplex.leftHomologyData' · cited by 4HomComplex.leftHomologyDa…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3InjectiveResolution.extEq…CochainComplex.HomComplex.CohomologyClass.descAddMonoidHom · cited by 2CohomologyClass.descAddMo…CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective · cited by 2CohomologyClass.equivOfIs…CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective · cited by 2CohomologyClass.equivOfIs…CochainComplex.HomComplex.CohomologyClass.mkAddMonoidHom · cited by 2CohomologyClass.mkAddMono…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveHasQuotient.Quotient · cited by 2301HasQuotient.QuotientCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cocycle · cited by 130HomComplex.CocycleCochainComplex.HomComplex.coboundaries · cited by 7HomComplex.coboundariesHomComplex.CohomologyClassCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by63

Results whose statement or proof uses this declaration.