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The Szendrei expansion of restriction semigroupoids
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- Journal:
- Glasgow Mathematical Journal , First View
- Published online by Cambridge University Press:
- 20 July 2026, pp. 1-23
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We introduce the concept of a restriction semigroupoid
$\mathcal{S}$, 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 certain category of partial maps. Furthermore, we construct the Szendrei expansion 
$Sz(\mathcal{S})$ of 
$\mathcal{S}$ and establish that each premorphism between two restriction semigroupoids 
$\mathcal{S}$ and 
$\mathcal{T}$ is uniquely factorized by a morphism between the Szendrei expansion 
$Sz(\mathcal{S})$ and 
$\mathcal{T}$.
