Theorems · Definition · group theory

groupHomology.H0Iso

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] → (A : Rep.{u, u, u} k G) → groupHomology.H0 A ≅ (Rep.coinvariantsFunctor k G).obj A

The 0th group homology of A, defined as the 0th homology of the complex of inhomogeneous chains, is isomorphic to the invariants of the representation on A.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree

Cited by

12 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroup