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# Feynman graphs, and nerve theorem for compact symmetric
multicategories (extended abstract)

By André Joyal and Joachim Kock
To appear in the proceedings of the "Quantum Physics and Logic VI"
(Oxford 2009), Electronic Notes in Theoretical Computer Science.
ArXiv:0908.2675.

#### Abstract

We describe a category of Feynman graphs and show how it relates to compact
symmetric multicategories (coloured modular operads) just as linear orders
relate to categories and rooted trees relate to multicategories. More
specifically we obtain the following nerve theorem: compact symmetric
multicategories can be characterised as presheaves on the category of Feynman
graphs subject to a Segal condition.
This text is a write-up of the second-named author's QPL6 talk;
a more detailed account of this material will
appear elsewhere.
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Last updated: 2010-02-20 by
Joachim Kock.