Mike Prest (University of Manchester) – Ultraproducts of rings, modules and tensor categories

Ultraproducts of rings and their modules have been appearing in various places in representation theory and the theory of tensor categories.  We consider how this is reflected in the model theory of modules over the rings and, in particular, we describe the effect on the lattices of pp formulas, definable subcategories, Ziegler spectra and the associated abelian categories of pp-imaginaries.  We also look at what happens when we enrich the picture with a monoidal = tensor product structure.