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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DOI: 10.1016/j.aim.2021.108011

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Abstract

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
Related URLs:	Publisher
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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