Theorems · Theorem · group theory

groupCohomology.map_id_comp_H0Iso_hom

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {A B : Rep.{u, u, u} k G} (f : A ⟶ B),
  CategoryTheory.CategoryStruct.comp (groupCohomology.map (MonoidHom.id G) f 0) (groupCohomology.H0Iso B).hom =
    CategoryTheory.CategoryStruct.comp (groupCohomology.H0Iso A).hom ((Rep.invariantsFunctor k G).map f)

Defined in: Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
Cited by: 2 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CommRingstatement and proof · cited by 17,173
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
CategoryTheory.Iso.homstatement and proof · cited by 7,684
Submodulestatement · cited by 7,192
CategoryTheory.Category.assocproof · cited by 6,433
Groupstatement and proof · cited by 6,238
ModuleCatstatement and proof · cited by 1,429
CategoryTheory.ShortComplex.X₁proof · cited by 889
Repstatement and proof · cited by 843

Cited by2

Results whose statement or proof uses this declaration.

groupCohomology.map_id_comp_H0Iso_hom_applyproof · cited by 0
groupCohomology.map_id_comp_H0Iso_hom_assocproof · cited by 0