Submission date: 9 November 2017

Abstract:

The correspondence between definable connected groupoids in a theory T and internal generalised imaginary sorts of T, established by Hrushovski in [Groupoids, imaginaries and internal covers, Turkish Journal of Mathematics, 2012], is here extended in two ways: First, it is shown that the correspondence is in fact an equivalence of categories, with respect to appropriate notions of morphism. Secondly, the equivalence of categories is shown to vary uniformly in definable families, with respect to an appropriate relativisation of these categories. Some elaboration on Hrushovki's original constructions are also included.

Mathematics Subject Classification: 03C45

Keywords and phrases: definable groupoids, internality, analysability

Full text arXiv 1711.03531: pdf, ps.