* revised paper available
@ 1997-02-19 15:52 categories
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From: categories @ 1997-02-19 15:52 UTC (permalink / raw)
To: categories
Date: Wed, 19 Feb 1997 12:17:32 +0100 (MET)
From: koslowj@iti.cs.tu-bs.de
Hello,
A revised version of my article "A convenient category for games and
interaction" is available from my home page
http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/koslowski.html
It better substantiates my claim of last year's workshop Domains II
here in Braunschweig that the composition of games I introduced is
orthogonal to the established composition of strategies. The abstract
is appended at the end.
If you had trouble in the past reaching my home page, we did find a
faulty entry in a name server last Fall. If the problems persist,
please let me know!
-- J"urgen
%% Abstract for: A convenient category for games and interaction
Guided by the familiar construction of the category rel of
relations, we first construct an order-enriched category gam .
Objects are sets, and 1-cells are games, viewed as special kinds of
trees. The quest for identities for the composition of arbitrary
trees naturally suggests alternating trees of a specific
orientation. Disjoint union of sets induces a tensor product
$\otimes$ and an operation --o on gam that allow us to
recover the monoidal closed category of games and strategies of
interest in game theory. Since gam does not have enough maps,
\ie, left adjoint 1-cells, these operations do not have nice
intrinsic descriptions in gam . This leads us to consider games
with explicit delay moves. To obtain the ``projection'' maps
lacking in gam , we consider the Kleisli-category K induced by
the functor _+1 on the category of maps in gam . Then we
extend gam as to have K as category of maps. Now a
satisfactory intrinsic description of the tensor product exists,
which also allows us to express --o in terms of simpler
operations. This construction makes clear why $\multimap$, the key
to the notion of strategy, cannot be functorial on gam .
Nevertheless, the composition of games may be viewed as orthogonal to
the familiar composition of strategies in a common framework.
--
J"urgen Koslowski % If I don't see you no more in this world
ITI % I meet you in the next world
TU Braunschweig % and don't be late!
koslowj@iti.cs.tu-bs.de % Jimi Hendrix (Voodoo Child)
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