Module discrete 

Discrete additive spaces and their group completion.

N supplies the additive natural-number monoid, while Z is its Grothendieck completion. The latter also acts as the lattice used to form the circle S1 as a quotient of the real line.

Structs

N

The natural numbers ℕ under addition — the free commutative monoid on one generator. Grothendieck-completed to Z to form the integer lattice.

Z

The integers ℤ, as the Grothendieck completion of N. Serves as the covering lattice for S1.