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SUMMARY:List objects with algebraic structure - Philip Saville (University
  of Cambridge)
DTSTART:20170523T131500Z
DTEND:20170523T141500Z
UID:TALK72548@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:It is well-known that the set of lists over a set X is the fre
 e monoid on X.\nThis is in fact true in any monoidal category\, for list o
 bjects defined as\nhaving an initiality property akin to primitive recursi
 on.  In certain\napplications to be discussed during the talk\, it is impo
 rtant to extend the\nnotion of monoid to that of T-monoid by further addin
 g a compatible\nmonad algebra structure to monoids.  Correspondingly\, the
  notion of list\nobject may be extended to that of T-list object by adding
  monad algebra\nstructure with respect to which the universal iterator is 
 a homomorphism.\nWe shall see that T-list objects give rise to free T-mono
 ids\, and consider\npractical settings where one can give an explicit cons
 truction of them in\nterms of initial algebras.  Finally\, I shall concent
 rate on an application\,\nintroducing a notion of near semiring category\,
  and showing how such\ncategories are an appropriate setting to consider o
 perads with compatible\nalgebraic structure. Along the way I will sketch a
  theory of parametrised\ninitiality for algebras\, and point out applicati
 ons to the theory of abstract\nsyntax.\nThis is joint work with Marcelo Fi
 ore.
LOCATION:MR5\, Centre for Mathematical Sciences
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