Theorems · Theorem · group theory

groupCohomology.cocyclesMap_id_comp_assoc

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {A B C : Rep.{u, u, u} k G} (φ : A ⟶ B) (ψ : B ⟶ C) (n : ℕ)
  {Z : ModuleCat k} (h : groupCohomology.cocycles C n ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (groupCohomology.cocyclesMap (MonoidHom.id G) (CategoryTheory.CategoryStruct.comp φ ψ) n) h =
    CategoryTheory.CategoryStruct.comp (groupCohomology.cocyclesMap (MonoidHom.id G) φ n)
      (CategoryTheory.CategoryStruct.comp (groupCohomology.cocyclesMap (MonoidHom.id G) ψ n) h)

Defined in: Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality
Cited by: 0 results in Mathlib
Foundations: Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites12

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.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
ModuleCatstatement and proof · cited by 1,429
Repstatement and proof · cited by 843
MonoidHom.idstatement and proof · cited by 323
Rep.resstatement · cited by 213
groupCohomology.cocyclesstatement and proof · cited by 63
groupCohomology.cocyclesMapstatement and proof · cited by 19
groupCohomology.cocyclesMap_id_compproof · cited by 1

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.