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arXiv · 2502.06610

The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties

Federico Campanini·Laura Cossu·Salvatore Tringali
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Abstract

We introduce and investigate the category $\mathsf{AtoMon}$ of atomic monoids and atom-preserving monoid homomorphisms, which is a (non-full) subcategory of the usual category of monoids. In particular, we compute all limits and colimits, showing that $\mathsf{AtoMon}$ is a complete and cocomplete category. We also address certain arithmetic properties of products and coproducts, providing explicit formulas for some fundamental invariants associated with factorization lengths in atomic monoids.

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Federico Campanini, Laura Cossu, Salvatore Tringali. 2025-02-10. The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties. https://arxiv.org/abs/2502.06610

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