Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories (Extended Abstract)

d abstract) Andr´e Joyal 1 D´epartement des math´ematiques Universit´e du Qu´ebec `a Montr´eal Canada Joachim Kock 2 3 Departament de matem`atiques Universitat Aut`onoma de Barcelona Spain 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 [9].

• Type: Journal
• Year: 2011
• Where: ENTCS
• Authors: André Joyal, Joachim Kock
• Keywords: Compact Symmetric Multicategories, ENTCS 2011, Feynman Graphs, Symmetric Multicategories