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arXiv · 2510.26660

A Categorical Realization of the (2-)Category of Monoids via Sch{\"u}tzenberger Categories and Strict Factorization Systems

Xavier Mary
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Abstract

We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on the Sch{\"u}tzenberger category of semigroups and categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital semigroups and semigroup homomorphisms. By introducing suitable natural transformations, we turn these equivalences into 2-equivalences between 2-categories. The 2-category $\mathbf{Mon_s^{(2)}}$ constructed this way proves the good one to study Morita equivalence of monoids.

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BibTeXRIS

Xavier Mary. 2025-10-30. A Categorical Realization of the (2-)Category of Monoids via Sch{\"u}tzenberger Categories and Strict Factorization Systems. https://arxiv.org/abs/2510.26660

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