Theorems · Theorem · group theory

groupHomology.map_id_comp_H0Iso_hom_apply

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {A B : Rep.{u, u, u} k G} (f : A ⟶ B)
  (x : ↑(groupHomology A 0)),
  (CategoryTheory.ConcreteCategory.hom (groupHomology.H0Iso B).hom)
      ((CategoryTheory.ConcreteCategory.hom (groupHomology.map (MonoidHom.id G) f 0)) x) =
    (Representation.Coinvariants.map A.ρ B.ρ (Rep.Hom.hom f))
      ((CategoryTheory.ConcreteCategory.hom (groupHomology.H0Iso A).hom) x)

Defined in: Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality
Cited by: 0 results in Mathlib
Foundations: Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites26

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

DFunLike.coestatement · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
LinearMapstatement · cited by 10,215
CategoryTheory.Functor.mapproof · cited by 8,698
CategoryTheory.Iso.homstatement and proof · cited by 7,684
Groupstatement and proof · cited by 6,238
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
ModuleCatstatement · cited by 1,429
ModuleCat.carrierstatement and proof · cited by 997

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.