2 papers
math.CT2025
Generalised ultracategories and conceptual completeness of geometric logic
Ali Hamad
We introduce the theory of generalised ultracategories, these are relational extensions to ultracategories as defined by Lurie. An essential example of generalised ultracategories…
math.CT2025
Ultracategories as colax algebras for a pseudo-monad on CAT
Ali Hamad
We show a result inspired by a conjecture by Shulman claiming that ultracategories as defined by Lurie are normal colax algebras for a certain pseudo-monad on the category of categ…