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CATEGORIES:Category Theory Seminar
SUMMARY:Free monads in double categories - Nicola Gambino\
, University of Palermo
DTSTART;TZID=Europe/London:20101102T141500
DTEND;TZID=Europe/London:20101102T151500
UID:TALK27551AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/27551
DESCRIPTION:The development of the formal theory of monads\, b
egun by\nStreet and later continued by Street and
Lack\, shows that large parts of the theory of mon
ads can be developed within an arbitrary 2-categor
y rather than in the 2-category of small categorie
s\, functors and natural transformations. I will d
escribe some joint work with Tom Fiore and Joachim
Kock in which we extend the basic concepts of the
formal theory of monads from the setting of 2-cat
egories to that of double categories. The motivati
on to do so derives from the desire to understand
better the universal properties of the free catego
ry on a graph and of the free monad on a polynomia
l endofunctor. Our main result shows that\, under
some mild conditions\, a double category that\nis
a framed bicategory admits the construction of fre
e monads if its horizontal 2-category does. After
explaining this result\, I will illustrate how it
can be applied to obtain double adjunctions that e
xtend the adjunction between graphs and categories
and the adjunction between polynomial endofunctor
s and polynomial monads.
LOCATION:MR3\, Centre for Mathematical Sciences
CONTACT:Nathan Bowler
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