2019/07/04 by Cianci, Nicolás
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1907.02624
We summarize several results about the regular coverings and the fundamental groupoids of Alexandroff spaces. In particular, we show that the fundamental groupoid of an Alexandroff space X is naturally isomorphic to the localization, at its set of morphisms, of the thin category associated to the set X considered as a preordered set with the specialization preorder. We also show that the regular coverings of an Alexandroff space X are represented by certain morphism-inverting functors with domain X, extending a result of E. Minian and J. Barmak about the regular coverings of locally finite T0 spaces.