Theorems · Theorem · group theory

ContinuousCohomology.map_comp

∀ {k : Type u} {G H K : Type v} [inst : Ring k] [inst_1 : TopologicalSpace k] [inst_2 : Group G]
  [inst_3 : TopologicalSpace G] [inst_4 : IsTopologicalGroup G] [inst_5 : Group H] [inst_6 : TopologicalSpace H]
  [inst_7 : IsTopologicalGroup H] [inst_8 : Group K] [inst_9 : TopologicalSpace K] [inst_10 : IsTopologicalGroup K]
  {X : TopRep k G} {Y : TopRep k H} {Z : TopRep k K} (φ : H →ₜ* G) (ψ : K →ₜ* H) (f : TopRep.res (↑φ) X ⟶ Y)
  (g : TopRep.res (↑ψ) Y ⟶ Z) (n : ℕ),
  ContinuousCohomology.map (φ.comp ψ) (CategoryTheory.CategoryStruct.comp ((TopRep.resFunctor ↑ψ).map f) g) n =
    CategoryTheory.CategoryStruct.comp (ContinuousCohomology.map φ f n) (ContinuousCohomology.map ψ g n)

Defined in

Mathlib.RepresentationTheory.Homological.ContCohomology.Functoriality

Cited by

1 results in Mathlib

Foundations

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

Assumes

RingTopologicalSpaceGroupTopologicalSpaceIsTopologicalGroupGroupTopologicalSpaceIsTopologicalGroupGroupTopologicalSpaceIsTopologicalGroup