Theorems · Theorem · group theory

groupHomology.pOpcycles_comp_opcyclesIso_hom

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.pOpcycles (groupHomology.inhomogeneousChains A) 0)
      (groupHomology.opcyclesIso₀ A).hom =
    CategoryTheory.CategoryStruct.comp (groupHomology.chainsIso₀ A).hom ((Rep.coinvariantsMk k G).app A)

Defined in: Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree
Cited by: 4 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group

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Cites33

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
RingHom.idstatement · cited by 18,349
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CommRingstatement and proof · cited by 17,173
LinearMapstatement · cited by 10,215
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.NatTrans.appstatement · cited by 7,406
Groupstatement and proof · cited by 6,238
HomologicalComplex.Xstatement · cited by 1,839
ModuleCatstatement · cited by 1,429
ModuleCat.carrierstatement · cited by 997

Cited by4

Results whose statement or proof uses this declaration.

groupHomology.π_comp_H0Iso_homproof · cited by 4
groupHomology.coinvariantsMk_comp_opcyclesIso₀_invproof · cited by 2
groupHomology.pOpcycles_comp_opcyclesIso_hom_applyproof · cited by 0
groupHomology.pOpcycles_comp_opcyclesIso_hom_assocproof · cited by 0