$\infty$-Operads as Analytic Monads
Algebraic Topology
2020-10-30 v3 Category Theory
Abstract
We develop an -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 -operads, namely -operads as analytic monads. We justify this definition by proving that the -category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for -operads.
Keywords
Cite
@article{arxiv.1712.06469,
title = {$\infty$-Operads as Analytic Monads},
author = {David Gepner and Rune Haugseng and Joachim Kock},
journal= {arXiv preprint arXiv:1712.06469},
year = {2020}
}
Comments
69 pages, v2: updated using results of arXiv:2002.01037, v3: accepted version