8 papers · 1 filter
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…
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…
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…
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