Heuts, G., Hinich, V. and Moerdijk, I. (2016) On the equivalence between Lurie's model and the dendroidal model for infinity-operads. Advances in Mathematics, 302. pp. 869-1043. ISSN 0001-8708
Abstract
© 2016 Elsevier Inc.We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and ∞-categories which replaces simplices by trees. The other is based on a certain homotopy theory of marked simplicial sets over the nerve of Segal's category Γ. In this paper we prove that for operads without constants these two theories are equivalent, in the precise sense of the existence of a zig-zag of Quillen equivalences between the respective model categories.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier. This is an author produced version of a paper subsequently published in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Simplicial operads; Dendroidal sets; Infinity-operads; Quillen model structures; Quillen equivalence; Forest sets |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Nov 2017 14:54 |
Last Modified: | 17 Nov 2017 14:58 |
Published Version: | https://doi.org/10.1016/j.aim.2016.07.021 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.aim.2016.07.021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124125 |