March 3, 2026Open Access

Conference on Rings and Polynomials 2025, TU Graz, Graz, Austria.

Key Points

Atomic monoids form a complete and cocomplete category with well-defined limits and colimits.
All limits and colimits in the atomic monoids category can be computed and verified successfully.
The research focuses on arithmetic properties of products and coproducts in atomic monoids.
The findings have implications for the broader understanding of monoid categories and their applications.

Abstract

The Category of Atomic Monoids. We study the category AtoMon of atomic monoids and atom-preserving maps, which is a (non-full) subcategory of the category Mon of monoids. We compute all limits and colimits, showing that AtoMon is both a complete and cocomplete category. Finally, we study some arithmetic properties of products and coproducts of atomic monoids. Based on a joint work with Laura Cossu and Salvatore Tringali.

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Campanini et al. (Wed,) studied this question.

www.synapsesocial.com/papers/69a75fccc6e9836116a2bc8e

Authors

Federico Campanini

Conference on inter- and transdisciplinary research for sustainable development 2025

Conference on Rings and Polynomials 2025, TU Graz, Graz, Austria.

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