7 papers
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…
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, s…
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…
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…