Advances in Commutative Ring Theory, Catania, Italy.

Key Points

AtoMon is shown to be both complete and cocomplete, which means it can form limits and colimits effectively.
Key findings include detailed computations regarding arithmetic properties of products and coproducts of atomic monoids.
Observation involved the category AtoMon, focusing on atom-preserving maps, which distinguishes it from the broader category Mon.
The findings highlight the importance of AtoMon's properties, indicating potential applications and further inquiries.

Abstract

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.

Advances in Commutative Ring Theory, Catania, Italy.

Key Points

Abstract

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