Operads as Analytic Monads
We develop an $\infty $-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\infty $-operads, namely $\infty $-operads as analytic monads. We justify this definition by proving that the...
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| Published in: | International mathematics research notices Vol. 2022; no. 16; pp. 12516 - 12624 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
06-08-2022
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| Online Access: | Get full text |
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| Summary: | We develop an $\infty $-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\infty $-operads, namely $\infty $-operads as analytic monads. We justify this definition by proving that the $\infty $-category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for $\infty $-operads. |
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| ISSN: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rnaa332 |