FoxDifferential.Completed.Continuous.Free

5 sections | 5 files | 39 declarations

Crossed differentials, universal differential modules, Fox boundaries, Euler formulas, and Jacobians are the common algebraic layer used by Crowell and metabelian applications.

CanonicalFormula

1 files | 3 declarations | 3 Theorem

Boundary-map form of the source-shaped completed Fox formula for the canonical free pro-\(C\) semidirect lift.

Continuity

1 files | 15 declarations | 15 Theorem

The completed Fox semidirect generator map is continuous when both component maps are continuous.

DiscreteGenerators

1 files | 4 declarations | 4 Theorem

Continuous completed Fox semidirect homomorphisms from a free pro-\(C\) source are unique for discrete generators, without a separate generator-continuity hypothesis.

Rules

1 files | 14 declarations | 12 Theorem | 2 Definition

The right component of the completed free pro-\(C\) Fox lift is bundled as a continuous homomorphism.

SourceFormula

1 files | 3 declarations | 3 Theorem

Source-shaped completed Fox boundary formula for continuous crossed differentials out of a free pro-\(C\) source.