Graphical combinatorics and a distributive law for modular operads

Raynor, Sophie (2021) Graphical combinatorics and a distributive law for modular operads. Advances in Mathematics, 392. 108011.

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This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit cycles, and are known for their complexity. In 2011, Joyal and Kock introduced a powerful graphical formalism for modular operads. This paper extends that work. A monad for modular operads is constructed and a corresponding nerve theorem is proved, using Weber's abstract nerve theory, in the terms originally stated by Joyal and Kock. This is achieved using a distributive law that sheds new light on the combinatorics of modular operads.

Item ID: 73427
Item Type: Article (Research - C1)
ISSN: 1090-2082
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Copyright Information: © 2021 Elsevier Inc. All rights reserved.
Funders: Australian Research Council (ARC)
Projects and Grants: ARC grant DP160101519
Date Deposited: 10 May 2022 02:48
FoR Codes: 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490403 Category theory, k theory, homological algebra @ 100%
SEO Codes: 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 100%
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