To an inverse semigroup, we associate an étale groupoid such that its actions on topological
spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow …

We provide three functorial extensions of the equivalence between localic étale groupoids
and their quantales. The main result is a biequivalence between the bicategory of localic …

Topological groupoids admit various types of morphisms. We push these notions to the level
of continuous groupoid actions to obtain various types of groupoid action morphisms. Some …

The purpose of this paper is to introduce a category whose objects are discrete dynamical
systems $(X, P, H,\theta) $ in the sense of [6] and whose arrows will be defined starting from …

Taking advantage of the quantale-theoretic description of étale groupoids we study principal
bundles, Hilsum–Skandalis maps, and Morita equivalence by means of modules on inverse …

We introduce a category of inverse semigroup actions and a category of\'etale groupoids.
We show that there are three functors which send inverse semigroups to their spectral …

By restricting to a class of localic open groupoids G which, similarly to Lie groupoids,
possess appropriate covers G ˆ→ G by étale groupoids, we extend results about groupoid …

We study Fell bundles on groupoids from the viewpoint of quantale theory. Given any
saturated upper semicontinuous Fell bundle π: E→ G on an étale groupoid G with G 0 …

In this work, the notion of a quantum inverse semigroup is introduced as a linearized
generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is …

By a map p: Q → X p: Q→ X of involutive quantales is meant a homomorphism p^*: X → Q
p∗: X→ Q. Calling a map p weakly open if p^* p∗ has a left adjoint p_! p! which satisfies the …