Categories meet semigroups in various ways
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915207468548096 |
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| author | Pécsi, Bertalan |
| author_facet | Pécsi, Bertalan |
| contents | This paper touches on several interaction points of semigroups and constructions from category theory: An adjunction is established between categories with selected arrows and semigroups. Regular semigroups are characterized by split epi - split mono factorization of the Karoubi envelope. We investigate how semigroupads (monads without requirement of unit transformation) map semigroups to semigroups and ensure certain properties provided they hold on meta level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categories meet semigroups in various ways Pécsi, Bertalan Category Theory 20M50 (Primary) 20M17, 18A32, 18C15 (Secondary) This paper touches on several interaction points of semigroups and constructions from category theory: An adjunction is established between categories with selected arrows and semigroups. Regular semigroups are characterized by split epi - split mono factorization of the Karoubi envelope. We investigate how semigroupads (monads without requirement of unit transformation) map semigroups to semigroups and ensure certain properties provided they hold on meta level. |
| title | Categories meet semigroups in various ways |
| topic | Category Theory 20M50 (Primary) 20M17, 18A32, 18C15 (Secondary) |
| url | https://arxiv.org/abs/2503.06711 |