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We describe a category of Feynman graphs and show how it relates to compactsymmetric multicategories (coloured modular operads) just as linear ordersrelate to categories and rooted trees relate to multicategories. Morespecifically we obtain the following nerve theorem: compact symmetricmulticategories can be characterised as presheaves on the category of Feynmangraphs subject to a Segal condition. This text is a write-up of thesecond-named author's QPL6 talk; a more detailed account of this material willappear elsewhere.

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