2019/09/11 by Adámek, Jirí, Sousa, Lurdes · 3 citations
#18A99 #18C15 #18C35 #18D10 #18D15 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.04950
For a number of locally finitely presentable categories K we describe the codensity monad of the full embedding of all finitely presentable objects into K. We introduce the concept of D-ultrafilter on an object, where D is a "nice" cogenerator of K. We prove that the codensity monad assigns to every object an object representing all D-ultrafilters on it. Our result covers e.g. categories of sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.