Generalised ultracategories and conceptual completeness of geometric logic
preprint
We introduce generalised ultracategories and use them to show a conceptual completeness theorem for geometric logic (infinitary coherent logic).
Publications
Ultracategories as colax algebras for a pseudo-monad on CAT
preprint
We show a result inspired by a conjecture by Shulman, stating that ultracategories as defined by Lurie, are colax algebras for a pseudomonad on the category of categories.
Bundles of metric structures as left ultrafunctors
preprint
We explore a new class of ultrcategories, those of complete metric structures, which can be better understood in the framework of continuous model theory, introddcing the notion of bundles of models, and showing it corresponds to a certain class of left ultrafunctors, this notion reduces to already known notions, like Banach bundles and Hilbert bundles.