Flat vs. filtered colimits

Giacomo Tendas – 27 January 2021

In the enriched context two different notions of accessibility have been introduced: one is a direct generalization of the ordinary definition, and involves only conical filtered colimits; the other involves colimits weighted by flat V-functors, a larger class of enriched “filtered” weights which includes the conical ones. An explicit characterization of the flat V-functor is then essential to better understand the relation between these two notions. The aim of this talk is to give such a characterization for some specific bases of enrichment including (among others) V = Set (of course), Cat, Gpd, sSet, Ab, and Gr (Ab).