Étale groupoids and their quantales

SGF-Quantales and their groupoids

Étale groupoids and their quantales

We establish a close and previously unknown relation between quantales and groupoids, in terms of which the notion of étale groupoid is subsumed in a natural way by that of quantale. 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, whic...

Quantales as geometric objects: symmetry beyond groupoids?

Modern mathematics has become pervaded by the idea that in order to cater for certain notions of symmetry, in particular of a local nature, one needs to go beyond group theory, replacing groups by groupoids. A nice survey of some implications of this idea in algebra, geometry, and analysis (as of 1996) can be found in [19]. The same idea can be expressed in terms of pseudogroups, which provide ...

Lectures on étale groupoids, inverse semigroups and quantales

complete pseudogroups L∨ bb

Polynomial evaluation groupoids and their groups

In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can beobtained as a polynomial evaluation groupoid.