We will continue on Thursday, September 19, in M5 at 1pm by the talk
J. Adamek
Ultrafilters in Locally Presentable Categories
Abstract: 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 Dultrafilter on an object, where D is a “nice” cogenerating object of K. Example: in Pos we choose the 2chain as D. A Dultrafilter on a poset X is a prime upset, closed under finite intersecitions, in the poset of all upsets of X.
We prove that the above codensity monad assigns to every object an object representing all Dultrafilters on it. Our result covers e.g. the categories of sets, vector spaces, posets, semilattices, graphs and Msets for finite commutative monoids M.
