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Article contents
Categories of graphs for operadic structures
Part of:
Applied homological algebra and category theory
Graph theory
Categories and geometry
Homotopy theory
Published online by Cambridge University Press: 28 September 2023
Abstract
We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalised 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 generalised operads can be realised at the level of presheaves. This includes adjunctions between operads and cyclic operads, between dioperads and augmented cyclic operads, and between wheeled properads and modular operads.
MSC classification
Primary:
18F20: Presheaves and sheaves
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 1 , January 2024 , pp. 155 - 212
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
Footnotes
†
This work was supported by a grant from the Simons Foundation (#850849).
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