3 papers
math.CT2023
On topological groupoids that represent theories
Joshua Wrigley
Grothendieck toposes, and by extension, logical theories, can be represented by topological structures. Butz and Moerdijk showed that every topos with enough points can be represen…
math.CT2023
The Geometric Completion of a Doctrine
Joshua Wrigley
As several different formal systems with inequivalent syntax may describe equivalent semantics, it is possible to find `completions' to more expressive syntaxes that are semantical…
math.AG2023
Some Properties of Internal Locale Morphisms Externalised
Joshua Wrigley
We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise tho…