Feynman graphs, and nerve theorem for compact symmetric multicategories (Extended Abstract)

André Joyal*, Joachim Kock

*Corresponding author for this work

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16 Citations (Scopus)


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 [André Joyal and Joachim Kock. Manuscript in preparation].

Original languageEnglish
Pages (from-to)105-113
Number of pages9
JournalElectronic Notes in Theoretical Computer Science
Issue number2
Publication statusPublished - 14 Feb 2011


  • Feynman graph
  • modular operad
  • monad
  • multicategory
  • nerve theorem

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