Pino Rosolini (Università degli Studi di Genova) will give a talk on
Structuring categories of models
Abstract:
In a paper in APAL in 1990, Michael Makkai introduced the notion of ultracategory and used it to characterise categories of models of pretoposes. The main theorem he produced (aka Conceptual Completeness Theorem) is an ample extension of Stone duality for Boolean algebras to (intuitionistic) first order theories. Later on, Jacob Lurie refined that notion of ultracategory, producing another approach to the duality for pretoposes, and was followed by other attempts.
In the talk, we shall recall Makkai’s and Lurie’s notions, providing examples and applications. Then, we shall introduce a pseudo-algebraic notion of structured category which relates the two previous kinds of ultracategories. We suggest how the various notions can be related, using recent results in the literature, and present some open problems.
This is joint work in progress with Richard Garner.