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Modules as exact functors

Prof. Mike Prest, University of Manchester

Donnerstag, 2017-07-06 17:00Uhr

A module - a linear representation of a ring (or other object) - can occur as a representation of many different rings (under Morita, or more generally tilting, equivalence, for example). This can be seen as choosing a different generator for an abelian category canonically associated to the module. From the point of view of model theory it is choosing a different home sort in the associated category of imaginaries. Through this we are led to an alternative view of what a module is, which I will illustrate with some examples and applications.