Subject: categories: preprint + CT99 photos

From: Koslowski <[email-masked]>
Date: Fri, 18 Feb 2000 14:35:42 +0100 (MET)

Dear Colleagues,

Together with Robin Cockett and Robert Seely I would like to announce
the availablility of a preprint 

	Morphisms and modules for linear bicategories

that has been submitted for the CT99 proceedings.  You can get it from
<http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/RESEARCH/>.  

Those interested in some of the pictures I took at that meeting may want
to look at <http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/PHOTOS/CT99-0/>.
If anybody wants his or her picture removed, or wants to order a print 
or a larger version of a picture, please let me know.

-- J"urgen Koslowski

Abstract:

  Linear bicategories are a generalization of bicategories, in which
  the horizontal composition of 1-cells is replaced by two (coherently
  linked) horizontal compositions.  This notion combines and
  integrates compositional features typical of bicategories with those
  arising from linear logic.  Linear bicategories, therefore, provide
  a natural categorical semantics and interpretation for (relational)
  non-commutative linear logic.  In particular, the logical notion of
  negation (or complementation) turns into a linear notion of
  adjunction, with involutive negations corresponding to cyclic linear
  adjunctions.  The latter are crucial for the construction of a
  tricategory of linear bicategories, linear functors, linear
  transformations and linear modifications.

  This paper first develops the structure of the afore-mentioned
  tricategory and describes how the various components have a natural
  interpretation using the diagrammatic calculus of circuits.  Then we
  transfer the module construction to the linear setting, which leads
  to a new linear bicategory of linear monads, linear modules, and
  module transformations over a given linear bicategory.  This lives
  in a tricategory where the 1-cells are given by linear functors that
  are strict on units.  The connections of this construction with the
  nucleus construction for linear bicategories are indicated at the end.
  
  The present paper is primarily expository, setting out the notions
  necessary for the development of category theory enriched in a
  linear bicategory.

-- 
J"urgen Koslowski           \  If I don't see you no more on this world
ITI, TU Braunschweig          \  I'll meet you on the next one
[email-masked]         \  and don't be late!
http://www.iti.cs.tu-bs/~koslowj  \     Jimi Hendrix (Voodoo Child, SR)