CompletedGroupAlgebra/AllFiniteAugmentation/TerminalIndex.lean
1import CompletedGroupAlgebra.Separation
3/-
4PUBLIC_PAGE_SNAPSHOT
5generated_at: 2026-05-27T09:47:29+09:00
6lean_source: lean4/CompletedGroupAlgebra/AllFiniteAugmentation/TerminalIndex.lean
7translation_root: data/translation
8purpose: identifies the local data snapshot used to build pages/
9placement: after imports, never before imports
10-/
11/-!
12# Completed group algebras
14The completed group algebra is presented as an inverse limit of finite group algebras, together with canonical augmentation, augmentation ideal, finite-stage maps, functoriality, and profinite module universal properties.
15-/
16open scoped Topology
18namespace CompletedGroupAlgebra
20noncomputable section
22open ProCGroups
23open ProCGroups.ProC
24open ProCGroups.InverseSystems
25open ProCGroups.Completion
27universe u v w
29variable (R : Type u) [CommRing R] [TopologicalSpace R] [IsTopologicalRing R]
30variable (G : Type v) [Group G] [TopologicalSpace G] [IsTopologicalGroup G]
31variable {H : Type v} [Group H] [TopologicalSpace H] [IsTopologicalGroup H]
34 (R : Type u) [CommRing R] [TopologicalSpace R] :
35 Nonempty (CompletedGroupAlgebraOpenQuotientIndex R G) :=
36 inferInstance
37end