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arXiv · 2606.30198

Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups

Tristan Bice·Malcolm Jones·Ganna Kudryavtseva
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Abstract

We extend the construction of Steinberg algebras of ample groupoids to \'etale semicategories. We also relate ample semicategories to Boolean restriction semigroups via a representation result extending previously known results for categories. Furthermore, we prove a reconstruction result which characterises an abstract algebra $A$ with a certain Cartan-like restriction subsemigroup $B$ (subject to conditions resembling those defining quasi-Cartan pairs) as the Steinberg algebra of the ultrafilter groupoid of $B$. In this way we obtain a twist-free extension of previous Steinberg algebra reconstruction results.

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Tristan Bice, Malcolm Jones, Ganna Kudryavtseva. 2026-06-29. Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups. https://arxiv.org/abs/2606.30198

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