Etale groupoids as germ groupoids and their base extensions

Reconstructing Etale Groupoids from Semigroups

We unify various étale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semigroup. 3) Steinberg's reconstruction from a groupoid ring. 4) Choi-Gardella-Thiel's reconstruction from a groupoid L^p-algebra. We do this by working with certain bumpy semigroups S of functions defined on an étale groupoid G. The semigroup structure of S together with the diagonal subsemigroup D then yields a natural domination relation < on S. The groupoid of <-ultrafilters is then isomorphic to the original groupo…

范畴中Étale群oid和伪群的极限

Limits in categories of étale groupoids and pseudogroups

本文证明了 sober Étale 群oid 和伪群范畴具有所有小极限，并给出了在该设置下 Cockett 和 Garner 伴随的另一种证明。

Sheaf theoretic characterization of etale groupoids

The study of Haeflier suggests that it is natural to regard a pseudogroup as an etale groupoid. We show that any etale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup. This correspondence is an analog of the equivalence of the two definitions of a sheaf: as an etale space and as a contravariant functor.