Theorems · Theorem · group theory

ContinuousCohomology.resolutionMap_comp_d

∀ {k : Type u} {G H : 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] {X : TopRep k G} {Y : TopRep k H} (φ : H →ₜ* G) (f : TopRep.res (↑φ) X ⟶ Y) (i : ℕ),
  CategoryTheory.CategoryStruct.comp (ContinuousCohomology.resolutionMap φ f i) (Y.d i) =
    CategoryTheory.CategoryStruct.comp ((TopRep.resFunctor ↑φ).map (X.d i))
      (ContinuousCohomology.resolutionMap φ f (i + 1))

The maps resolutionMap φ f commute with the differentials of the resolutions.

Defined in

Mathlib.RepresentationTheory.Homological.ContCohomology.Functoriality

Cited by

0 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceGroupTopologicalSpaceIsTopologicalGroupGroupTopologicalSpaceIsTopologicalGroup