Theorems · Theorem · group theory

groupHomology.H1CoresCoinf_exact

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) (S : Subgroup G) [inst_2 : S.Normal],
  (groupHomology.H1CoresCoinf A S).Exact

Given a G-representation A and a normal subgroup S ≤ G, the degree 1 corestriction-coinflation sequence H₁(S, A) ⟶ H₁(G, A) ⟶ H₁(G ⧸ S, A_S) is exact. simps squeezed for performance.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality

Cited by

0 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.Normal