Equivalences for the (2-)categories of monoids and unital semigroups
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915587068788736 |
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| author | Mary, Xavier |
| author_facet | Mary, Xavier |
| contents | We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalences for the (2-)categories of monoids and unital semigroups Mary, Xavier Category Theory Rings and Algebras 20M10, 18A32 We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on 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. |
| title | Equivalences for the (2-)categories of monoids and unital semigroups |
| topic | Category Theory Rings and Algebras 20M10, 18A32 |
| url | https://arxiv.org/abs/2510.26660 |