ProCGroups.CompletedGroupAlgebra.AllFiniteAugmentation

5 sections | 5 files | 37 declarations

This aggregate exports terminal-index and finite-stage augmentations, the canonical all-finite augmentation, its comparison with the \(C\)-indexed augmentation, and the completed augmentation ideal.

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AugmentationIdeal

1 file | 14 declarations | 13 Theorems | 1 Definition
This file defines the kernel of the canonical augmentation on the all-finite completed group algebra, packages its short exact sequence, and proves comparison and functoriality ...

CanonicalAugmentation

1 file | 13 declarations | 11 Theorems | 2 Definitions
This module defines the all-finite canonical augmentation as the composition of a terminal finite-stage augmentation with the canonical bundled projection, and proves that it ca...

InClassComparison

1 file | 2 declarations | 2 Theorems
The canonical comparison maps between the all-finite and in-class completions commute with their augmentations. This file records both directions of that compatibility.

StageAugmentation

1 file | 7 declarations | 6 Theorems | 1 Definition
This file defines augmentation on each finite coefficient-and-group stage of the all-finite system and proves its formulas on basis elements and compatibility with transition, c...

TerminalIndex

1 file | 1 declaration | 1 Instance
This file constructs a canonical inhabitant of the open-quotient index used by the all-finite completed group algebra, ensuring that its inverse system is nonempty.