revised paper available

[categories <cat-dist@mta.ca>]

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)