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 ---------------------------------------------------------------------- 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.

Dear Peter, Superb! This is wonderful, and surely a must-have for anyone doing anything with structured monoidal categories. Your colourful picture of a diagram in a bicategory also made me laugh. For years I've been amazed at people who call multicategories "coloured operads" - the objects of the multicategory are "colours" to them. (For consistency, they ought to call categories "coloured monoids".) And there, you did a picture of it! Tom

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

---------------------------------------------------------------------- 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.

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