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Theorems · Definition · category theory

CochainComplex.HomComplex.Cochain.ofHom

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

The 0-cochain attached to a morphism of cochain complexes.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
121 results in Mathlib
Foundations
Depth 41 from the axioms, rests on 530 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.Cochain.ofHom_v · cited by 46Cochain.ofHom_vCochainComplex.HomComplex.Cocycle.ofHom · cited by 23Cocycle.ofHomCochainComplex.mappingCone.desc · cited by 19mappingCone.descCochainComplex.mappingCone.map · cited by 19mappingCone.mapCochainComplex.HomComplex.Cocycle.ofHom_coe · cited by 19Cocycle.ofHom_coeCochainComplex.mappingCone.liftCochain · cited by 18mappingCone.liftCochainCochainComplex.mappingCone.lift · cited by 12mappingCone.liftCochainComplex.mappingCocone.lift · cited by 8mappingCocone.liftCochainComplex.mappingCone.descCocycle · cited by 8mappingCone.descCocycleCochainComplex.mappingCone.inr_f_desc_f · cited by 8mappingCone.inr_f_desc_fCochainComplex.HomComplex.Cochain.equivHomotopy · cited by 8Cochain.equivHomotopyCochainComplex.mappingCone.mapOfHomotopy · cited by 7mappingCone.mapOfHomotopyCochainComplex.mappingCocone.desc · cited by 6mappingCocone.descCochainComplex.mappingCone.descCocycle_coe · cited by 6mappingCone.descCocycle_c…CochainComplex.mappingCone.liftCocycle · cited by 6mappingCone.liftCocycleCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomologicalComplex.Hom.f · cited by 845Hom.fCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainCochainComplex.HomComplex.Cochain.ofHoms · cited by 8Cochain.ofHomsCochain.ofHomCITED BYCITES

Cites8

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Cited by141

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