categories: request for comments: "A survey of graphical languages for monoidal categories"

categories: request for comments: "A survey of graphical languages for monoidal categories"

[Peter Selinger]

Dear Category Theorists,

as you know, there is a proliferation of monoidal categories with
additional structure, many of which have graphical languages. For
example: autonomous, balanced, braided, compact closed, pivotal,
ribbon, rigid, sovereign, spherical, tortile, traced.

I have recently written a survey article on all of these graphical
languages (and more). The goal was not to re-prove known theorems, but
simply to collect most known facts in one location, with references to
the primary literature. I have also tried to put a systematic
perspective on things. Consequently, I included many results and
conjectures that don't seem to appear in the literature at all, or for
which only special cases seem to be known.

Since this paper will not be refereed in the usual sense (it is
supposed to appear as a book chapter), I am instead inviting comments
and corrections from all interested parties. I am particularly
interested in missing references for any of the results or
conjectures, and of course any other corrections you might have.

The article is available from:
http://www.mathstat.dal.ca/~selinger/papers.html#graphical

I hope this will be useful. Thanks! -- Peter

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P. Selinger: A survey of graphical languages for monoidal categories

December 2008. 59 pages.

Abstract: This article is intended as a reference guide to various
notions of monoidal categories and their associated string
diagrams. It is hoped that this will be useful not just to
mathematicians, but also to physicists, computer scientists, and
others who use diagrammatic reasoning. We have opted for a somewhat
informal treatment of topological notions, and have omitted most
proofs. Nevertheless, the exposition is sufficiently detailed to make
it clear what is presently known, and to serve as a starting place for
more in-depth study. Where possible, we provide pointers to more
rigorous treatments in the literature. Where we include results that
have only been proved in special cases, we indicate this in the form
of caveats.