Abstract
We compare two models for (Formula presented.) -operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison results already in the literature, this implies that all known models for (Formula presented.) -operads are equivalent — for instance, it follows that the homotopy theory of Lurie's (Formula presented.) -operads is equivalent to that of dendroidal sets and that of simplicial operads.
| Original language | English |
|---|---|
| Pages (from-to) | 857-873 |
| Number of pages | 17 |
| Journal | Journal of Topology |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Dec 2018 |
Funding
Received 6 July 2016; revised 8 March 2018; published online 6 August 2018. 2010 Mathematics Subject Classification 18D50, 55U35 (primary). The first author thanks Denis-Charles Cisinski, David Gepner, and especially his PhD advisor Markus Spitzweck for helpful discussions. Moreover, he wishes to acknowledge the support of the DFG during his PhD and of the Labex CEMPI (ANR-11-LABX-0007-01) during his postdoc. The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682922).
Keywords
- Mathematics - Algebraic Topology
- Mathematics - Category Theory