Theorems · Theorem · group theory

groupCohomology.map_H0Iso_hom_f

∀ {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),
  CategoryTheory.CategoryStruct.comp (groupCohomology.map f φ 0)
      (CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso B).hom (groupCohomology.shortComplexH0 B).f) =
    CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom
      (CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f (Rep.Hom.toModuleCatHom φ))

Defined in

Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality

Cited by

3 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupGroup