Actions of etale-covered groupoids

JOURNAL OF ALGEBRA

卷:566

Article

Quijano, Juan Pablo¹  Resende, Pedro¹ 

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

关键词: Localic open groupoids;    Groupoid quantales;    Actions;    Sheaves;    Bi-actions;   

DOI  :  10.1016/j.jalgebra.2020.08.032

来源: Elsevier

【 摘 要 】

By restricting to a class of localic open groupoids G which, similarly to Lie groupoids, possess appropriate covers (G) over cap -> G by etale groupoids, we extend results about groupoid actions and quantales that were previously proved for etale groupoids but do not seem to work for arbitrary open groupoids. In particular we obtain a characterization of the category of G-actions as a category of quantale modules on O((G) over cap) that satisfy a condition related to the quantale O(G). This leads to a simple description of G-sheaves and the classifying topos of G in terms of Hilbert O((G) over cap)-modules. The bicategory whose 1-cells are the groupoid bi-actions is bi-equivalent to a corresponding bicategory of quantales and bimodules. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free