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CATEGORIES:Category Theory Seminar
SUMMARY:List objects with algebraic structure - Philip Sav
ille (University of Cambridge)
DTSTART;TZID=Europe/London:20170523T141500
DTEND;TZID=Europe/London:20170523T151500
UID:TALK72548AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72548
DESCRIPTION:It is well-known that the set of lists over a set
X is the free monoid on X.\nThis is in fact true i
n any monoidal category\, for list objects defined
as\nhaving an initiality property akin to primiti
ve recursion. In certain\napplications to be disc
ussed during the talk\, it is important to extend
the\nnotion of monoid to that of T-monoid by furth
er adding a compatible\nmonad algebra structure to
monoids. Correspondingly\, the notion of list\no
bject may be extended to that of T-list object by
adding monad algebra\nstructure with respect to wh
ich the universal iterator is a homomorphism.\nWe
shall see that T-list objects give rise to free T-
monoids\, and consider\npractical settings where o
ne can give an explicit construction of them in\nt
erms of initial algebras. Finally\, I shall conce
ntrate on an application\,\nintroducing a notion o
f near semiring category\, and showing how such\nc
ategories are an appropriate setting to consider o
perads with compatible\nalgebraic structure. Along
the way I will sketch a theory of parametrised\ni
nitiality for algebras\, and point out application
s to the theory of abstract\nsyntax.\nThis is join
t work with Marcelo Fiore.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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