The many groupoids of a stably Gelfand quantale

JOURNAL OF ALGEBRA

卷:498

Article

Resende, Pedro¹ 

[1] Univ Lisbon, Ctr Anal Matemat Geometria & Sistemas Dinam, Inst Super Tecn, Dept Matemat, Av Rovisco Pais 1, P-1049001 Lisbon, Portugal

关键词: Stably Gelfand quantales;    Pseudogroups;    Inverse quantal frames;    Etale groupoids;   

DOI  :  10.1016/j.jalgebra.2017.11.042

来源: Elsevier

【 摘 要 】

We study the projections of an arbitrary stably Gelfand quantale Q and show that each projection determines a pseudogroup S subset of Q (and a corresponding localic etale groupoid G) together with a map of involutive quantales p : Q -> L-V (S) [= 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 Q whose partial units cover Q. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free