Theorems · Theorem · group theory

groupHomology.chainsMap_f

∀ {k G H : Type u} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] {A : Rep.{u, u, u} k G}
  {B : Rep.{u, u, u} k H} (f : G →* H) (φ : A ⟶ Rep.res f B) (i : ℕ),
  (groupHomology.chainsMap f φ).f i =
    CategoryTheory.CategoryStruct.comp (ModuleCat.ofHom (Finsupp.lmapDomain (↑A) k fun x => ⇑f ∘ x))
      (ModuleCat.ofHom (Finsupp.mapRange.linearMap (Rep.Hom.hom φ).toLinearMap))

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality

Cited by

9 results in Mathlib

Foundations

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

Assumes

CommRingGroupGroup