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arXiv · 1706.06545

The many groupoids of a stably Gelfand quantale

Pedro Resende
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Abstract

We study the projections of an arbitrary stably Gelfand quantale $Q$ and show that each projection determines a pseudogroup $S\subset Q$ (and a corresponding localic \'etale groupoid $G$) together with a map of involutive quantales $p:Q\to\mathcal L^{\bigvee}(S)\ [=\mathcal O(G)]$. As an application we obtain a simplified axiomatization of inverse quantal frames (= quantales of \'etale groupoids) whereby such a quantale is shown to be the same as a unital stably Gelfand quantal frame whose partial units cover $Q$.

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Pedro Resende. 2017-06-20. The many groupoids of a stably Gelfand quantale. https://doi.org/10.1016/j.jalgebra.2017.11.042

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