Theorems · Definition · group theory

groupHomology.inhomogeneousChainsIso

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) →
        [DecidableEq G] →
          groupHomology.inhomogeneousChains A ≅ HomologicalComplex.coinvariantsTensorObj A (Rep.barComplex k G)

Given a k-linear G-representation A, the complex of inhomogeneous chains is isomorphic to (A ⊗[k] P)_G, where P is the bar resolution of k as a trivial G-representation.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Basic

Cited by

0 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupDecidableEq