Theorems · Theorem · group theory

groupHomology.inhomogeneousChains.d_eq

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) (n : ℕ) [inst_2 : DecidableEq G],
  groupHomology.inhomogeneousChains.d A n =
    CategoryTheory.CategoryStruct.comp (A.coinvariantsTensorFreeLEquiv (Fin (n + 1) → G)).toModuleIso.inv
      (CategoryTheory.CategoryStruct.comp
        ((HomologicalComplex.coinvariantsTensorObj A (Rep.barComplex k G)).d (n + 1) n)
        (A.coinvariantsTensorFreeLEquiv (Fin n → G)).toModuleIso.hom)

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Basic

Cited by

0 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupDecidableEq