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arXiv · 2411.06633

Categorical representation of DRC-semigroups

James East·Matthias Fresacher·P. A. Azeef Muhammed·Timothy Stokes
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Abstract

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.

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James East, Matthias Fresacher, P. A. Azeef Muhammed, Timothy Stokes. 2024-11-11. Categorical representation of DRC-semigroups. https://arxiv.org/abs/2411.06633

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