Theorems · Definition · group theory

groupCohomologyIsoExt

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) →
        (n : ℕ) → groupCohomology A n ≅ ((Ext k (Rep.{u, u, u} k G) n).obj (Opposite.op (Rep.trivial k G k))).obj A

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

Defined in

Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingGroup