Theorems · Definition · group theory

groupHomology.H2Iso

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) → groupHomology.H2 A ≅ (groupHomology.shortComplexH2 A).moduleCatLeftHomologyData.H

The 2nd group homology of A, defined as the 2nd homology of the complex of inhomogeneous chains, is isomorphic to cycles₂ A ⧸ boundaries₂ A, which is a simpler type.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree

Cited by

6 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroup