Subject: categories: paper announcement

From: Koslowski <[email-masked]>
Date: Mon, 1 Feb 1999 01:00:07 +0100 (MET)

A heavily revised version of my paper "Beyond the Chu-construction"
is now available from my home page:

	http://www.iti.cs.tu-bs.de/~koslowj/RESEARCH/

It will eventually be published in Applied Categorical Structures.
I have not attempted to attribute the term "dualizing object" to anyone
in particular.  The open problem of an earlier version, as to whether
Cauchy-complete bicategories of interpolads inherit local *-autonomy 
from their base, has been answered affirmatively.  

Here is the abstract:

  Starting from symmetric monoidal closed (= autonomous) categories,
  Po-Hsiang Chu showed how to construct new *-autonomous categories,
  i.e., autonomous categories that are self-dual because of a
  dualizing object.  Recently, Michael Barr extended this to the
  non-symmetric, but closed, case, utilizing monads and modules
  between them.  Since these notions are well-understood for
  bicategories, we introduce a notion of local *-autonomy for these
  that implies closedness and, moreover, is inherited when forming
  bicategories of monads and of interpolads.  Since the initial step
  of Barr's construction also carries over to the bicategorical
  setting, we recover his main result as an easy corollary.
  Furthermore, the Chu-construction at this level may be viewed as a
  procedure for turning the endo-1-cells of a closed bicategory into
  the objects of a new closed bicategory, and hence conceptually is
  similar to constructing bicategories of monads and of interpolads.

Best regards,

-- J"urgen

-- 
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!
[email-masked] %              Jimi Hendrix (Voodoo Child)