FoxDifferential.Completed.FreeProC.Uniqueness

5 sections | 5 files | 23 declarations

Free pro-C sources are treated through completed Fox derivatives, stage projections, density arguments, and semidirect lift formulas.

Derivative

1 files | 5 declarations | 5 Theorem

Any continuous semidirect lift with the prescribed generator components has the canonical free pro-\(C\) completed Fox derivative vector as its left component.

Existence

1 files | 3 declarations | 3 Theorem

Existence and uniqueness of the free pro-\(C\) completed Fox derivative vector, formulated as the left component of a continuous semidirect homomorphism with prescribed generato...

Lift

1 files | 6 declarations | 6 Theorem

Continuous completed Fox semidirect lifts from a free pro-\(C\) source are unique once their generator values are prescribed.

Morphism

1 files | 5 declarations | 5 Theorem

Categorical completed Fox semidirect morphisms from a free pro-\(C\) source are unique once their generator values are prescribed.

SemidirectHom

1 files | 4 declarations | 3 Theorem | 1 Definition

A completed crossed differential and its coefficient homomorphism combine into a semidirect homomorphism.