| Title:
|
A horn-like characterization of the fibrant objects in the minimal model structure on simplicial sets (English) |
| Author:
|
Feller, Matt |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
7 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
166-181 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the fibrant objects in the minimal model structure on the category of simplicial sets are characterized by a lifting condition with respect to maps which resemble the horn inclusions that define Kan complexes. (English) |
| Keyword:
|
Minimal model structure |
| Keyword:
|
simplicial sets |
| MSC:
|
18N40 |
| MSC:
|
18N50 |
| idZBL:
|
Zbl 1532.18014 |
| idMR:
|
MR4600459 |
| DOI:
|
10.21136/HS.2023.05 |
| . |
| Date available:
|
2026-03-13T10:11:31Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153460 |
| . |
| Reference:
|
[1] Ara, D.: Higher quasi-categories vs higher Rezk spaces.Journal of K-Theory, Vol. 14, Iss. 3, 701-749 MR 3350089 |
| Reference:
|
[2] Balchin, S.: A handbook of model categories.Springer, Volume 27 MR 4385504 |
| Reference:
|
[3] Campbell, A., Lanari, E.: On truncated quasi-categories.Cahiers Topol. Géom. Différ. Catég., Vol. 61, Iss. 2, 157-207 MR 4504075 |
| Reference:
|
[4] Cisinski, D.-C.: Les préfaisceaux comme type d’homotopie.Soc. Math. France, Volume 308 |
| Reference:
|
[5] Cisinski, D.-C.: Higher categories and homotopical algebra.Cambridge University Press, Volume 180 MR 3931682 |
| Reference:
|
[6] Feller, M.: Generalizing quasi-categories via model structures on simplicial sets.Preprint MR 4885568 |
| Reference:
|
[7] Feller, M.: Quasi-2-Segal sets.Tunisian Journal of Math. MR 4596737 |
| Reference:
|
[8] Hirschhorn, P.: Model categories and their localizations.American Mathematical Society, Volume 99 Zbl 1017.55001, MR 1944041 |
| Reference:
|
[9] Hovey, M.: Model categories.American Mathematical Society, Volume 63 |
| Reference:
|
[10] Joyal, A.: The theory of quasi-categories and its applications.Lecture notes |
| Reference:
|
[11] Quillen, D.: Homotopical algebra.Lecture Notes in Mathematics, Vol. 43, Iss. 43 |
| . |
