Theorems · Definition · group theory

groupHomologyIsoTor

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) →
        [DecidableEq G] → (n : ℕ) → groupHomology A n ≅ ((Rep.Tor k G n).obj A).obj (Rep.trivial k G k)

The nth group homology of a k-linear G-representation A is isomorphic to Torₙ(A, k) (taken in Rep k G), where k is a trivial k-linear G-representation.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Basic

Cited by

1 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupDecidableEq