Functoriality and uniformity in Hrushovski's groupoid-cover correspondence
Logic
2017-11-10 v1
Abstract
The correspondence between definable connected groupoids in a theory and internal generalised imaginary sorts of , 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.
Keywords
Cite
@article{arxiv.1711.03531,
title = {Functoriality and uniformity in Hrushovski's groupoid-cover correspondence},
author = {Levon Haykazyan and Rahim Moosa},
journal= {arXiv preprint arXiv:1711.03531},
year = {2017}
}