Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/109766
Type: | Journal article |
Title: | Covariant model structures and simplicial localization |
Author: | Stevenson, D. |
Citation: | North-Western European Journal of Mathematics, 2017; 3:141-202 |
Publisher: | Laboratoire Paul Painlevé |
Issue Date: | 2017 |
ISSN: | 2496-5170 |
Statement of Responsibility: | Danny Stevenson |
Abstract: | In this paper we prove that for any simplicial set B, there is a Quillen equiv- alence between the covariant model structure on S/B and a certain localization of the projective model structure on the category of simplicial presheaves on the simplex category ∆/B of B. We extend this result to give a new Quillen equivalence between this covariant model structure and the projective model structure on the category of simplicial presheaves on the simplicial category C[B]. We study the relationship with Lurie’s straightening theorem. Along the way we also prove some results on localizations of simplicial categories and quasi-categories. |
Keywords: | Quasi-categories; Left fibrations; covariant model structure; simplicial categories; simplicial localization |
Rights: | Authors keep their copyrights. Thus they can reuse figures, article parts or any material they need for subsequent work. The contract license is the Creative Commons License CC-BY which is the most flexible contract maximising the readership on publication. |
Grant ID: | http://purl.org/au-research/grants/arc/DP120100106 |
Published version: | http://math.univ-lille1.fr/~nwejm/OnlinePapers/Archives/Archives.php |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_109766.pdf | Published version | 561.67 kB | Adobe PDF | View/Open |
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