Theorems · Theorem · group theory

groupCohomology.map_H0Iso_hom_f_apply

∀ {k G H : Type u} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] {A : Rep.{u, u, u} k H}
  {B : Rep.{u, u, u} k G} (f : G →* H) (φ : Rep.res f A ⟶ B) (x : ↑(groupCohomology A 0)),
  (CategoryTheory.ConcreteCategory.hom (groupCohomology.shortComplexH0 B).f)
      ((CategoryTheory.ConcreteCategory.hom (groupCohomology.H0Iso B).hom)
        ((CategoryTheory.ConcreteCategory.hom (groupCohomology.map f φ 0)) x)) =
    (Rep.Hom.hom φ).toLinearMap
      ((CategoryTheory.ConcreteCategory.hom (groupCohomology.shortComplexH0 A).f)
        ((CategoryTheory.ConcreteCategory.hom (groupCohomology.H0Iso A).hom) x))

Defined in

Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupGroup