Theorems · Definition · group theory

groupCohomology.inhomogeneousCochainsIso

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) → groupCohomology.inhomogeneousCochains A ≅ (Rep.barComplex k G).linearYonedaObj k A

Given a k-linear G-representation A, the complex of inhomogeneous cochains is isomorphic to Hom(P, A), where P is the bar resolution of k as a trivial G-representation.

Defined in

Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingGroup