5 papers · 1 filter
Representation of abstract pseudogroups
Joshua L. Wrigley
The Wagner-Preston theorem states that every inverse semigroup can be embedded into an inverse semigroup of partial bijections on some set. However, this embedding does not respect…
A counterexample to Kanalas' problem of continuously realising types
Morgan Rogers, Joshua Wrigley
We give an example of a coherent theory, a topological space, and a continuous assignment of the (model-theoretic) types of the theory to the points of the space, such that there i…
The points of canonical extensions of doctrines
Sam van Gool, Joshua L. Wrigley
We analyse the space of points of the canonical extension of a coherent doctrine. We first give a full characterisation of doctrine morphisms that are extensible, and relate it to…
Locales in presheaf toposes vs. presheaves of locales
Vasileios Aravantinos-Sotiropoulos, Panagis Karazeris, Joshua Wrigley
By a well-known characterisation, in a presheaf topos every internal suplattice is a presheaf of suplattices, but not every presheaf of suplattices is an internal suplattice (and s…
Generic bundles over a localic category
Graham Manuell, Joshua L. Wrigley
In this paper we construct classifying localic categories and groupoids for various bundles equipped with logical structure. When these bundles are local homeomorphisms, we recover…