12 papers
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…
Existential completions and Herbrand's theorem
Joshua L. Wrigley
Recently, Abbadini and Guffanti gave an algebraic proof of Herbrand's theorem using a completion for Lawvere doctrines that freely adds existential and universal quantifiers. A mor…
On the theories classified by an étendue
Joshua Wrigley
We give a model-theoretic characterisation of the geometric theories classified by étendues -- the `locally localic' topoi. They are the theories where each model is determined, sy…
Ultracategories via Kan extensions of relative monads
Umberto Tarantino, Joshua Wrigley
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, u…
Day algebras
Edmund Robinson, Joshua Wrigley
In this paper we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This ge…
Topoi with enough points and topological groupoids
Joshua Wrigley
We establish a bi-equivalence between the bi-category of topoi with enough points and a localisation of a bi-subcategory of topological groupoids
Existentially closed models and locally zero-dimensional toposes
Mark Kamsma, Joshua Wrigley
The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models ex…
The representing localic groupoid for a geometric theory
Graham Manuell, Joshua L. Wrigley
We give an expository, and hopefully approachable, account of the Joyal-Tierney result that every topos can be represented as a topos of sheaves on a localic groupoid. We give an e…