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 vThe type of cohomology classes of degree n in the complex of morphisms
from K to L.
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HasQuotient.Quotientproof · cited by 2,301
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cocycleproof · cited by 130
- CochainComplex.HomComplex.coboundariesproof · cited by 7
Cited by63
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.CohomologyClass.mkstatement · cited by 34
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClassstatement · cited by 19
- CategoryTheory.InjectiveResolution.extEquivCohomologyClassstatement · cited by 19
- CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHomstatement and proof · cited by 10
- CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClassstatement and proof · cited by 9
- CategoryTheory.InjectiveResolution.extAddEquivCohomologyClassstatement and proof · cited by 9
- CochainComplex.HomComplex.CohomologyClass.mk_surjectivestatement · cited by 7
- CochainComplex.HomComplex.CohomologyClass.toHomstatement · cited by 6
- CochainComplex.HomComplex.leftHomologyData'proof · cited by 4
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_homstatement · cited by 3
- CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_homstatement · cited by 3
- CochainComplex.HomComplex.CohomologyClass.descAddMonoidHomstatement · cited by 2