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