Extending Hrushovski's groupoid-cover correspondence using simplicial groupoids
arXiv:2009.13870 · doi:10.1016/j.apal.2021.102970
Abstract
Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure of the 1-analysable covers of a theory T using simplicial groupoids definable in T is realized here. The ideas of Haykazyan and Moosa, found in ["Functoriality and uniformity in Hrushovski's groupoid-cover correspondence," Annals of Pure and Applied Logic , 2018] are used, and extended, to define an equivalence of categories. Finally, a couple of examples are studied with these new tools.
55 pages, made the author name consistent with other submissions