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Theorems · Definition · category theory

CochainComplex.HomComplex.Cocycle.ofHom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {F G : CochainComplex C ℤ} → (F ⟶ G) → CochainComplex.HomComplex.Cocycle F G 0

The 0-cocycle associated to a morphism in CochainComplex C ℤ.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
23 results in Mathlib
Foundations
Depth 57 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.Cocycle.ofHom_coe · cited by 19Cocycle.ofHom_coeCochainComplex.mappingCone.desc · cited by 19mappingCone.descCochainComplex.mappingCocone.inr · cited by 11mappingCocone.inrCochainComplex.mappingCocone.lift · cited by 8mappingCocone.liftCochainComplex.mappingCone.inr_f_desc_f · cited by 8mappingCone.inr_f_desc_fCochainComplex.mappingCone.inl_v_desc_f · cited by 5mappingCone.inl_v_desc_fCochainComplex.HomComplex.Cocycle.equivHom · cited by 4Cocycle.equivHomCochainComplex.mappingCone.rotateHomotopyEquiv · cited by 4mappingCone.rotateHomotop…CochainComplex.HomComplex.Cocycle.equivHomShift_apply · cited by 2Cocycle.equivHomShift_app…CochainComplex.mappingCocone.lift_f_fst_f · cited by 2mappingCocone.lift_f_fst_fCochainComplex.HomComplex.δ_ofHom_comp · cited by 1HomComplex.δ_ofHom_compCochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_self · cited by 1Cocycle.ofHom_homOf_eq_se…CochainComplex.mappingCone.lift_desc_f · cited by 1mappingCone.lift_desc_fCochainComplex.mappingCocone.inr_v_fst_f · cited by 1mappingCocone.inr_v_fst_fCochainComplex.mappingCocone.inr_v_snd_v · cited by 1mappingCocone.inr_v_snd_vCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cocycle · cited by 130HomComplex.CocycleCochainComplex.HomComplex.Cochain.ofHom · cited by 121Cochain.ofHomCochainComplex.HomComplex.Cocycle.mk · cited by 6Cocycle.mkCocycle.ofHomCITED BYCITES

Cites8

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Cited by28

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