Theorems · Definition · group theory

groupHomology.H1CoresCoinf

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] → Rep.{u, u, u} k G → (S : Subgroup G) → [S.Normal] → CategoryTheory.ShortComplex (ModuleCat k)

The short complex H₁(S, A) ⟶ H₁(G, A) ⟶ H₁(G ⧸ S, A_S). The first map is the "corestriction" map induced by the inclusion ι : S →* G and the identity on Res(ι)(A), and the second map is the "coinflation" map induced by the quotient maps G →* G ⧸ S and A →ₗ A_S.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality

Cited by

6 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.Normal