On the spectrum of monoids and semilattices

TL;DR

This paper shows that the Spec functor on commutative monoids is representable, enabling explicit calculation of Spec(M) for finitely generated monoids and exploring related consequences.

Contribution

It demonstrates the representability of the Spec functor on commutative monoids and provides a method for explicit computation for finitely generated cases.

Findings

Spec(M) can be explicitly calculated for finitely generated monoids

The functor Spec is representable on the category of commutative monoids

Several consequences of this representability are discussed

Abstract

Our main observation is that the contravariant functor Spec on the category of commutative monoids is representable. We discuss a few consequences of this fact. In particular, we give an efficient way of calculating the Spec(M) of a finitely generated monoid explicitly.