Categorical representation of DRC-semigroups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917833355558912 |
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| author | East, James Fresacher, Matthias Muhammed, P. A. Azeef Stokes, Timothy |
| author_facet | East, James Fresacher, Matthias Muhammed, P. A. Azeef Stokes, Timothy |
| contents | DRC-semigroups model associative systems with domain and range operations, and contain many important classes, such as inverse, restriction, Ehresmann, regular $*$-, and $*$-regular semigroups. In this paper we show that the category of DRC-semigroups is isomorphic to a category of certain biordered categories whose object sets are projection algebras in the sense of Jones. This extends the recent groupoid approach to regular $*$-semigroups of the first and third authors. We also establish the existence of free DRC-semigroups by constructing a left adjoint to the forgetful functor into the category of projection algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorical representation of DRC-semigroups East, James Fresacher, Matthias Muhammed, P. A. Azeef Stokes, Timothy Rings and Algebras Category Theory DRC-semigroups model associative systems with domain and range operations, and contain many important classes, such as inverse, restriction, Ehresmann, regular $*$-, and $*$-regular semigroups. In this paper we show that the category of DRC-semigroups is isomorphic to a category of certain biordered categories whose object sets are projection algebras in the sense of Jones. This extends the recent groupoid approach to regular $*$-semigroups of the first and third authors. We also establish the existence of free DRC-semigroups by constructing a left adjoint to the forgetful functor into the category of projection algebras. |
| title | Categorical representation of DRC-semigroups |
| topic | Rings and Algebras Category Theory |
| url | https://arxiv.org/abs/2411.06633 |