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Categories of graphs for operadic structures

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arxiv 2109.06231 v2 pith:RHWILUNA submitted 2021-09-13 math.CT math.AT

Philip Hackney This is my paper · ORCID
classification math.CTmath.AT
keywords operadscategoriescyclicadjunctionsgeneralizedgraphsmodularproperads
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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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Cited by 1 Pith paper

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  1. 2-dimensional TFTs via modular $\infty$-operads

    math.CT 2025-06 conditional novelty 7.0 of 10

    Constructs a modular ∞-operad of surfaces and a genus filtration showing 2D TFTs in a general target are modular algebras, producing a spectral sequence for mapping class group cohomology.

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