Give a point-free classification of torsors for topological or localic groupoids

Develop a point-free interpretation compatible with geometric logic that classifies torsors for general topological or localic groupoids.

Background

The paper discusses a result showing that, for suitable connected localic groups, ordinary sheaf toposes cannot classify all torsors over localic spaces. This failure is not merely a limitation of the particular construction associated with a groupoid; it can rule out the existence of any classifying topos in the ordinary sense.

The authors note that alternative frameworks, such as topological stacks, may classify torsors for general topological or localic groups, but it is unresolved whether such classifications admit the point-free, geometric-logical interpretation central to the paper. The problem extends this issue from groups to groupoids.

References

Can the classification of $G$-torsors for general topological/localic groupoids $G$ be given a point-free interpretation, compatible with geometric logic?

— The Archimedean place is a blurred interval at infinity  (2609.09117 - Ng, 8 Sep 2026) in Section 4, Subsection “What do Classifying Toposes Classify?”, Problem prob:Gbundles

Of course, other frameworks for classifying $G$-torsors exist (e.g. topological stacks ), but it is less clear if they have a point-free interpretation in the sense that was important to this paper (cf. Definition~\ref{def:ptFREEspace}).

— The Archimedean place is a blurred interval at infinity  (2609.09117 - Ng, 8 Sep 2026) in Section 4, Subsection “What do Classifying Toposes Classify?”, discussion following Observation obs:Lurie