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Theorems · Definition · category theory

CochainComplex.HomComplex.cocycle

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      (F G : CochainComplex C ℤ) → (n : ℤ) → AddSubgroup (CochainComplex.HomComplex.Cochain F G n)

The subgroup of cocycles in Cochain F G n.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
105 results in Mathlib
Foundations
Depth 53 from the axioms, rests on 1,106 definitions · 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.Cocycle · cited by 130HomComplex.CocycleCochainComplex.HomComplex.Cocycle.ext · cited by 19Cocycle.extCochainComplex.HomComplex.Cocycle.ofHom_coe · cited by 19Cocycle.ofHom_coeCochainComplex.HomComplex.Cocycle.homOf_f · cited by 13Cocycle.homOf_fCochainComplex.mappingCone.lift · cited by 12mappingCone.liftCochainComplex.mappingCone.inr_f_fst_v · cited by 9mappingCone.inr_f_fst_vCochainComplex.mappingCone.descCocycle · cited by 8mappingCone.descCocycleCochainComplex.mappingCone.inl_v_fst_v · cited by 7mappingCone.inl_v_fst_vCochainComplex.HomComplex.Cocycle.fromSingleMk_coe · cited by 7Cocycle.fromSingleMk_coeCochainComplex.HomComplex.Cocycle.toSingleMk_coe · cited by 7Cocycle.toSingleMk_coeCochainComplex.mappingCocone.desc · cited by 6mappingCocone.descCochainComplex.mappingCone.descCocycle_coe · cited by 6mappingCone.descCocycle_c…CochainComplex.HomComplex.Cocycle.cochain_ofHom_homOf_eq_coe · cited by 6Cocycle.cochain_ofHom_hom…CochainComplex.mappingCone.inl_v_fst_v_assoc · cited by 6mappingCone.inl_v_fst_v_a…CochainComplex.mappingCone.liftCocycle · cited by 6mappingCone.liftCocycleCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveAddSubgroup · cited by 3232AddSubgroupCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainAddMonoidHom.ker · cited by 158AddMonoidHom.kerLinearMap.toAddMonoidHom · cited by 101LinearMap.toAddMonoidHomCochainComplex.HomComplex.δ_hom · cited by 6HomComplex.δ_homHomComplex.cocycleCITED BYCITES

Cites8

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Cited by113

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