continuousCohomology — Mathlib

English

There is a natural isomorphism between continuousCohomology 0 and invariants: continuousCohomology 0 ≅ invariants.

Русский

Существует естественный изоморфизм между нулевой степенью непрерывной когомологий и инвариантами: continuousCohomology 0 ≅ invariants.

LaTeX

$$$\\text{continuousCohomology } R\\ G\\ 0 \\cong \\text{invariants } R\\ G$$$

Lean4

/-- `continuousCohomology R G n` is the functor taking
an `R`-linear `G`-representation to its `n`-th continuous cohomology. -/
noncomputable def _root_.continuousCohomology (n : ℕ) : Action (TopModuleCat R) G ⥤ TopModuleCat R :=
  homogeneousCochains R G ⋙ HomologicalComplex.homologyFunctor _ _ n

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