The Szendrei Expansion of Restriction Semigroupoids
Rings and Algebras
2025-04-30 v1
Abstract
We introduce the concept of a restriction semigroupoid S, which unifies the notion of restriction semigroups and restriction categories within a single structure. We prove a representation theorem, showing that every restriction semigroupoid can be embedded into a determined category of partial maps. Furthermore, we construct the Szendrei expansion Sz(S) of S and establish that each premorphism between two restriction semigroupoids S and T is uniquely factorized by a morphism between the Szendrei expansion Sz(S) and T.
Keywords
Cite
@article{arxiv.2504.20217,
title = {The Szendrei Expansion of Restriction Semigroupoids},
author = {Rafael Haag and Wesley G. Lautenschlaeger and Thaísa Tamusiunas},
journal= {arXiv preprint arXiv:2504.20217},
year = {2025}
}