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Theorems · Definition · category theory

CochainComplex.HomComplex.Cochain.comp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {F G K : CochainComplex C ℤ} →
        {n₁ n₂ n₁₂ : ℤ} →
          CochainComplex.HomComplex.Cochain F G n₁ →
            CochainComplex.HomComplex.Cochain G K n₂ → n₁ + n₂ = n₁₂ → CochainComplex.HomComplex.Cochain F K n₁₂

The composition of cochains.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
115 results in Mathlib
Foundations
Depth 51 from the axioms, rests on 813 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.comp_v · cited by 30Cochain.comp_vCochainComplex.mappingCone.descCochain · cited by 20mappingCone.descCochainCochainComplex.mappingCone.map · cited by 19mappingCone.mapCochainComplex.mappingCone.liftCochain · cited by 18mappingCone.liftCochainCochainComplex.HomComplex.Cochain.comp_zero_cochain_v · cited by 17Cochain.comp_zero_cochain…CochainComplex.HomComplex.Cochain.zero_cochain_comp_v · cited by 17Cochain.zero_cochain_comp…CochainComplex.mappingCone.lift · cited by 12mappingCone.liftCochainComplex.mappingCone.descCocycle · cited by 8mappingCone.descCocycleCochainComplex.HomComplex.Cochain.comp_assoc_of_second_is_zero_cochain · cited by 7Cochain.comp_assoc_of_sec…CochainComplex.mappingCone.mapOfHomotopy · cited by 7mappingCone.mapOfHomotopyCochainComplex.HomComplex.Cochain.zero_comp · cited by 7Cochain.zero_compCochainComplex.mappingCocone.desc · cited by 6mappingCocone.descCochainComplex.mappingCone.descCocycle_coe · cited by 6mappingCone.descCocycle_c…CochainComplex.mappingCone.liftCocycle · cited by 6mappingCone.liftCocycleCochainComplex.HomComplex.Cochain.comp_add · cited by 6Cochain.comp_addCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainCochainComplex.HomComplex.Cochain.v · cited by 213Cochain.vCochainComplex.HomComplex.Cochain.mk · cited by 8Cochain.mkCochain.compCITED BYCITES

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Cited by133

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