کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667964 1345489 2007 63 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Étale groupoids and their quantales
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Étale groupoids and their quantales
چکیده انگلیسی

We establish close and previously unknown relations between quantales and groupoids. In particular, to each étale groupoid, either localic or topological, there is associated a unital involutive quantale. We obtain a bijective correspondence between localic étale groupoids and their quantales, which are given a rather simple characterization and here are called inverse quantal frames. We show that the category of inverse quantal frames is equivalent to the category of complete and infinitely distributive inverse monoids, and as a consequence we obtain a (non-functorial) correspondence between these and localic étale groupoids that generalizes more classical results concerning inverse semigroups and topological étale groupoids. This generalization is entirely algebraic and it is valid in an arbitrary topos. As a consequence of these results we see that a localic groupoid is étale if and only if its sublocale of units is open and its multiplication map is semiopen, and an analogue of this holds for topological groupoids. In practice we are provided with new tools for constructing localic and topological étale groupoids, as well as inverse semigroups, for instance via presentations of quantales by generators and relations. The characterization of inverse quantal frames is to a large extent based on a new quantale operation, here called a support, whose properties are thoroughly investigated, and which may be of independent interest.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 208, Issue 1, 15 January 2007, Pages 147-209