Two models for the homotopy theory of ∞-operads

Hongyi Chu; Rune Haugseng; Gijs Heuts

doi:10.1112/topo.12071

Two models for the homotopy theory of ∞-operads

Hongyi Chu, Rune Haugseng, Gijs Heuts

Institut for Matematiske Fag

5 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Topology
Vol/bind	11
Udgave nummer	4
Sider (fra-til)	857-873
ISSN	1753-8416
DOI	https://doi.org/10.1112/topo.12071
Status	Udgivet - dec. 2018

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10.1112/topo.12071

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T1 - Two models for the homotopy theory of ∞-operads

AU - Chu, Hongyi

AU - Haugseng, Rune

AU - Heuts, Gijs

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N2 - 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.

AB - 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.

U2 - 10.1112/topo.12071

DO - 10.1112/topo.12071

M3 - Journal article

SN - 1753-8416

VL - 11

SP - 857

EP - 873

JO - Journal of Topology

JF - Journal of Topology

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ER -

Two models for the homotopy theory of ∞-operads

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