5 papers · 1 filter
Cellular generation revisited
Sean Cox, Mark Kamsma, JiÅà Rosický
Cellular generation, which generalises cofibrant generation, is an important categorical smallness condition on a class of morphisms. A general challenge is to determine whether a…
Cofibrant generation of pure monomorphisms in presheaf categories
Sean Cox, Jonathan Feigert, Mark Kamsma +2
We characterise when the pure monomorphisms in a presheaf category are cofibrantly generated in terms of the category . In particular, when…
Lifting independence along functors
Mark Kamsma, JiÅà Rosický
Given a functor and a model-theoretic independence relation on , we can lift that independence relation along to by…
Unstable independence from the categorical point of view
Mark Kamsma, JiÅà Rosický
We give a category-theoretic construction of simple and NSOP-like independence relations in locally finitely presentable categories, and in the more general locally finitely mu…
Existentially closed models and locally zero-dimensional toposes
Mark Kamsma, Joshua Wrigley
The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models ex…