Equivalences for the (2-)categories of monoids and unital semigroups

2025/10/30 by Mary, Xavier
#18A32 #20M10 #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.26660

Abstract

We construct a category equivalent to the category Mon of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category 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 Mon_s² constructed this way proves the good one to study Morita equivalence of monoids.

Citations

• Toposes of Discrete Monoid Actions

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