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Theorems · Definition · category theory

CochainComplex.HomComplex

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] → CochainComplex C ℤ → CochainComplex C ℤ → CochainComplex AddCommGrpCat ℤ

The cochain complex of homomorphisms between two cochain complexes F and G. In degree n : ℤ, it consists of the abelian group HomComplex.Cochain F G n.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
10 results in Mathlib
Foundations
Depth 56 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.leftHomologyData · cited by 4HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData' · cited by 4HomComplex.leftHomologyDa…CochainComplex.HomComplex.homologyAddEquiv · cited by 0HomComplex.homologyAddEqu…CochainComplex.HomComplex.leftHomologyData'_H_coe · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData'_K_coe · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData'_i · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData'_π · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData_H_coe · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData_K_coe · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex_X · cited by 0CochainComplex.HomComplex…CochainComplex.HomComplex_d_hom_apply · cited by 0CochainComplex.HomComplex…CochainComplex.HomComplex.leftHomologyData_i_hom_apply · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.leftHomologyData_π_hom_apply · cited by 0HomComplex.leftHomologyDa…CochainComplex.HomComplex.Cocycle.isKernel · cited by 0Cocycle.isKernelCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexComplexShape.Rel · cited by 518ComplexShape.RelAddCommGrpCat · cited by 462AddCommGrpCatCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainAddMonoidHomClass.toAddMonoidHom · cited by 232AddMonoidHomClass.toAddMo…AddCommGrpCat.of · cited by 97AddCommGrpCat.ofAddCommGrpCat.ofHom · cited by 72AddCommGrpCat.ofHomCochainComplex.HomComplex.δ_hom · cited by 6HomComplex.δ_homCochainComplex.HomComplexCITED BYCITES

Cites11

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Cited by14

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