Theorems · Definition · group theory

ContinuousCohomology.cochainsMap

{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) → (TopRep.res (↑φ) X ⟶ Y) → (X.homogeneousCochains ⟶ Y.homogeneousCochains)

The cochain map homogeneousCochains X ⟶ homogeneousCochains Y induced by a continuous group homomorphism φ : H →ₜ* G and a morphism of topological H-representations f : res φ X ⟶ Y, sending an invariant function σ : C(G, C(G, ⋯)) to f ∘ σ ∘ φ.

Defined in

Mathlib.RepresentationTheory.Homological.ContCohomology.Functoriality

Cited by

8 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceGroupTopologicalSpaceIsTopologicalGroupGroupTopologicalSpaceIsTopologicalGroup