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Announce paper: Cockett & Seely
The following paper has been placed on anonymous ftp at
triples.math.mcgill.ca, directory /pub/rags/wk_dist_cat
Weakly distributive categories
by J.R.B. Cockett and R.A.G. Seely
Abstract:
There are many situations in logic, theoretical computer science, and
category theory where two binary operations---one thought of as a (tensor)
``product'', the other a ``sum''---play a key role. In distributive and
*-autonomous categories these operations can be regarded as, respectively,
the and/or of traditional logic and the times/par of (multiplicative) linear
logic. In the latter logic, however, the distributivity of product over sum
is conspicuously absent: this paper studies a ``linearization'' of that
distributivity which is present in both case. Furthermore, we show that
this weak distributivity is precisely what is needed to model Gentzen's cut
rule (in the absence of other structural rules) and can be strengthened in
two natural ways to generate full distributivity and *-autonomous categories.
This is the journal version of the similarly named paper appearing in the
Proceedings of the Durham conference (1991):
M.P. Fourman, P.T. Johnstone, A.M. Pitts, eds., Applications of Categories
to Computer Science, London Mathematical Society Lecture Note Series 177
(1992) 45 - 65.
This version is to appear in the Journal of Pure and Applied Algebra.
The paper has been rewritten, including more details and several examples,
including shifted tensors, Span categories, and categories of modules of a
bialgebra.