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CATEGORIES:Category Theory Seminar
SUMMARY:Composition in Categories of Games - Nathan Bowler
\, DPMMS
DTSTART;TZID=Europe/London:20091201T141500
DTEND;TZID=Europe/London:20091201T154500
UID:TALK20995AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20995
DESCRIPTION:A common intuitive construction of categories of g
ames encodes the basic combinatorics involved in v
arious approaches to the study of games\, for exam
ple Conway's recursively structured theory\, or th
e specialised theory of hypergraph games. These id
eas have provided some key examples of models of (
various fragments of) intuitionistic and linear lo
gic. Such categories have also been used to constr
uct denotational semantics for various abstract pr
ogramming languages\, including the construction o
f a fully abstract model for PCF.\n\nI'll begin by
outlining how this intuitive construction works.
I'll give an example of such a category (based on
bicoloured digraphs) which allows the incorporatio
n of some of the structure of the theory of hyperg
raph games\, and I'll explain how this constructio
n points to the language of fc-multicategories as
a natural setting for the development of additiona
l structure in categories of games. This language
also provides a new setting for the construction o
f existing categories of games. I'll illustrate ho
w the constructions in this setting have a modular
form\, cleanly separating different aspects of th
e underlying combinatorics\, and I'll sketch some
possible applications to the development of new co
nstructions.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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