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Title: Compact symmetric multicategories and the problem of loops
Author: Raynor, Sophia C.
ISNI:       0000 0004 7228 7194
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2018
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The compact symmetric multicategories (CSMs) introduced by Joyal and Kock in their 2011 note 'Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories' [JK11] directly generalise a number of unital operad types, such as wheeled properads, that admit a contraction operation as well as an operadic multiplication. These structures are known to exhibit strange behaviour related to the contraction of units, and this is problematic for [JK11]. In this thesis, I modify the construction of [JK11] to obtain non unital (coloured) modular operads as algebras for a monad defined in terms of connected graphs, and use this as a foundation for a new construction of CSMs based on special graph morphisms. A corresponding nerve theorem characterises CSMs in terms of a Segal condition. This construction sheds light, and provides some control, on the behaviour of the contracted units.
Supervisor: Not available Sponsor: École polytechnique fédérale de Lausanne (EPFL)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Categories (Mathematics) ; Loops (Group theory)