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CATEGORIES:Category Theory Seminar
SUMMARY:D-ultrafilter monads - Lurdes Sousa (CMUC\, Univer
sity of Coimbra &\; IP Viseu)
DTSTART;TZID=Europe/London:20200211T141500
DTEND;TZID=Europe/London:20200211T151500
UID:TALK138325AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138325
DESCRIPTION:The ultrafilter monad on sets is the codensity mon
ad of the embedding of finite sets into Set\, as p
roved by Kennison and Gildenhuys (1971). In\nthis
talk I will present a notion of D-ultrafilter on a
n object of a category K\nwhich generalizes the on
e of an ultrafilter on a set\, where D is a cogene
rator\nof K. Working in a complete\, symmetric mon
oidal closed category\, with a\n‘nice cogenerator
D\, the corresponding D-ultrafilter monad is the c
odensity monad of the embedding of finitely presen
table objects of K\;\nmoreover\, it is a submonad
of the double-dualization monad relative to D.\nTh
is is illustrated by several examples\, including
commutative varieties and\ncategories of posets an
d graphs. I will also discuss a generalization wit
h the\nabove embedding replaced by the embedding o
f a small\nfull subcategory into a complete catego
ry\, with A containing a cogenerating\nset of K. T
his is based on joint work with Jiri Adámek.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:José Siqueira
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