Theorems · Theorem · group theory

groupHomology.cyclesMap_comp_assoc

∀ {k : Type u} [inst : CommRing k] {G H K : Type u} [inst_1 : Group G] [inst_2 : Group H] [inst_3 : Group K]
  {A : Rep.{u, u, u} k G} {B : Rep.{u, u, u} k H} {C : Rep.{u, u, u} k K} (f : G →* H) (g : H →* K)
  (φ : A ⟶ Rep.res f B) (ψ : B ⟶ Rep.res g C) (n : ℕ) {Z : ModuleCat k} (h : groupHomology.cycles C n ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (groupHomology.cyclesMap (g.comp f) (CategoryTheory.CategoryStruct.comp φ (Rep.resMap f ψ)) n) h =
    CategoryTheory.CategoryStruct.comp (groupHomology.cyclesMap f φ n)
      (CategoryTheory.CategoryStruct.comp (groupHomology.cyclesMap g ψ n) h)

Defined in: Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality
Cited by: 0 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group Group Group

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Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CommRingstatement and proof · cited by 17,173
CategoryTheory.Category.assocproof · cited by 6,433
Groupstatement and proof · cited by 6,238
MonoidHomstatement and proof · cited by 3,629
ModuleCatstatement and proof · cited by 1,429
Repstatement and proof · cited by 843
MonoidHom.compstatement and proof · cited by 469
Rep.resstatement and proof · cited by 213
groupHomology.cyclesstatement and proof · cited by 66
Rep.resMapstatement and proof · cited by 23

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