Graphical combinatorics and a distributive law for modular operads

Raynor, Sophie

doi:10.48550/arxiv.1911.05914

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Directed Graphs and The Wheeled Properadic Graphical Category1

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2021

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“…This category controls wheeled properads [MMS09] (which extend the notion of properad [Val07] to encode traces) in the sense that there is a relevant nerve theorem. Wheeled properads can be regarded as modular operads with additional directional structure, which was observed in [Rayb,Example 1.29].…”

Section: Directed Graphs and The Wheeled Properadic Graphical Categorymentioning

confidence: 99%

Categories of graphs for operadic structures

Hackney

2021

Preprint

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We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalized operads (e.g. cyclic operads, modular operads, properads, and so on), and give new, uniform definitions for their morphisms. This allows for straightforward comparisons, and we use this to show that certain free-forgetful adjunctions between categories of generalized operads can be realized at the level of presheaves. This includes adjunctions between operads and cyclic operads, between dioperads and augmented cyclic operads, and betweeen wheeled properads and modular operads.

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Section: Directed Graphs and The Wheeled Properadic Graphical Categorymentioning

confidence: 99%

Categories of graphs for operadic structures

Hackney

2021

Preprint

View full text Add to dashboard Cite

show abstract

Graphical combinatorics and a distributive law for modular operads

Cited by 1 publication

References 0 publications

Categories of graphs for operadic structures

Categories of graphs for operadic structures

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