Moser, Lyne and Sarazola, Maru (2024) A model structure for Grothendieck fibrations. JOURNAL OF PURE AND APPLIED ALGEBRA, 228 (10): 107692. ISSN 0022-4049, 1873-1376
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We construct two model structures, whose fibrant objects capture the notions of discrete fibrations and of Grothendieck fibrations over a category C. For the discrete case, we build a model structure on the slice Cat/C, Quillen equivalent to the projective model structure on [Cop, Set] via the classical category of elements construction. The cartesian case requires the use of markings, and we define a model structure on the slice Cat+/C, Quillen equivalent to the projective model structure on [Cop, Cat] via a marked version of the Grothendieck construction. We further show that both of these model structures have the expected interactions with their infinity-counterparts; namely, with the contravariant model structure on sSet/NC and with Lurie's cartesian model structure on sSet+/NC. (c) 2024 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Dec 2025 08:47 |
| Last Modified: | 04 Dec 2025 08:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64364 |
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