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SUMMARY:D-ultrafilter monads - Lurdes Sousa (CMUC\, University of Coimbra 
 &amp\; IP Viseu)
DTSTART:20200211T141500Z
DTEND:20200211T151500Z
UID:TALK138325@talks.cam.ac.uk
CONTACT:José Siqueira
DESCRIPTION:The ultrafilter monad on sets is the codensity monad of the em
 bedding of finite sets into Set\, as proved by Kennison and Gildenhuys (19
 71). In\nthis talk I will present a notion of D-ultrafilter on an object o
 f a category K\nwhich generalizes the one of an ultrafilter on a set\, whe
 re D is a cogenerator\nof K. Working in a complete\, symmetric monoidal cl
 osed category\, with a\n‘nice cogenerator D\, the corresponding D-ultraf
 ilter monad is the codensity monad of the embedding of finitely presentabl
 e objects of K\;\nmoreover\, it is a submonad of the double-dualization mo
 nad relative to D.\nThis is illustrated by several examples\, including co
 mmutative varieties and\ncategories of posets and graphs. I will also disc
 uss a generalization with the\nabove embedding replaced by the embedding o
 f a small\nfull subcategory into a complete category\, with A containing a
  cogenerating\nset of K. This is based on joint work with Jiri Adámek.
LOCATION:MR4\, Centre for Mathematical Sciences
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