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Theorems · Definition · group theory

groupCohomology.iCocycles

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) → (n : ℕ) → groupCohomology.cocycles A n ⟶ (groupCohomology.inhomogeneousCochains A).X n

The natural inclusion of the n-cocycles Zⁿ(G, A) into the n-cochains Cⁿ(G, A).

Defined in
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic
Cited by
27 results in Mathlib
Foundations
Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

groupCohomology.cocyclesIso₀_hom_comp_f · cited by 6groupCohomology.cocyclesI…groupCohomology.isoCocycles₁_hom_comp_i · cited by 5groupCohomology.isoCocycl…groupCohomology.isoCocycles₂_hom_comp_i · cited by 5groupCohomology.isoCocycl…groupCohomology.map_H0Iso_hom_f · cited by 3groupCohomology.map_H0Iso…groupCohomology.π_comp_H0IsoOfIsTrivial_hom · cited by 2groupCohomology.π_comp_H0…groupCohomology.isoCocycles₁_inv_comp_iCocycles · cited by 2groupCohomology.isoCocycl…groupCohomology.cocyclesIso₀_hom_comp_f_assoc · cited by 2groupCohomology.cocyclesI…groupCohomology.cocyclesIso₀_inv_comp_iCocycles · cited by 2groupCohomology.cocyclesI…groupCohomology.isoCocycles₂_inv_comp_iCocycles · cited by 2groupCohomology.isoCocycl…groupCohomology.cocyclesMap_cocyclesIso₀_hom_f · cited by 2groupCohomology.cocyclesM…groupCohomology.cocyclesMk₁_eq · cited by 2groupCohomology.cocyclesM…groupCohomology.isoCocycles₁_hom_comp_i_assoc · cited by 1groupCohomology.isoCocycl…groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply · cited by 1groupCohomology.isoCocycl…groupCohomology.cocyclesIso₀_hom_comp_f_apply · cited by 1groupCohomology.cocyclesI…groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply · cited by 1groupCohomology.cocyclesI…Quiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingGroup · cited by 6238GroupHomologicalComplex.X · cited by 1839HomologicalComplex.XModuleCat · cited by 1429ModuleCatComplexShape.up · cited by 1123ComplexShape.upRep · cited by 843RepgroupCohomology.inhomogeneousCochains · cited by 83groupCohomology.inhomogen…HomologicalComplex.iCycles · cited by 80HomologicalComplex.iCyclesgroupCohomology.cocycles · cited by 63groupCohomology.cocyclesgroupCohomology.iCocyclesCITED BYCITES

Cites10

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Cited by27

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