| Title:
|
Cartesian factorization systems and pointed cartesian fibrations of $\infty$-categories (English) |
| Author:
|
Lanari, Edoardo |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
5 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
1-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The goal of this paper is to prove an equivalence between the $(\infty,2)$-category of {\it cartesian} factorization systems on $\infty$-categories and that of {\it pointed} cartesian fibrations of $\infty$-categories. This generalizes a similar result known for ordinary categories and sheds some light on the interplay between these two seemingly distant concepts. (English) |
| Keyword:
|
Homotopy Theory |
| Keyword:
|
Higher Category Theory |
| MSC:
|
18G30 |
| MSC:
|
18G55 |
| MSC:
|
55U10 |
| MSC:
|
55U35 |
| idZBL:
|
Zbl 1481.18031 |
| idMR:
|
MR4367216 |
| DOI:
|
10.21136/HS.2021.01 |
| . |
| Date available:
|
2026-03-13T05:25:53Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153433 |
| . |
| Reference:
|
[1] Cisinski, Denis-Charles: Higher categories and homotopical algebra.Cambridge Studies in Advanced Mathematics, vol. 180, Cambridge University Press, Cambridge MR 3931682 |
| Reference:
|
[2] Gepner, David, Haugseng, Rune, Nikolaus, Thomas: Lax colimits and free fibrations in ∞-categories.Doc. Math. 22, 1225–1266 MR 3690268 |
| Reference:
|
[3] Joyal, André: Notes on quasi-categories.Preprint |
| Reference:
|
[4] Lurie, Jacob: (∞,2)-categories and the Goodwillie Calculus I.Preprint |
| Reference:
|
[5] Lurie, Jacob: Higher Topos Theory.Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ MR 2522659 |
| Reference:
|
[6] Riehl, E., Verity, D.: Fibrations and yoneda lemma in an ∞-cosmos.Journal of Pure and Applied Algebra 221, no. 3 MR 3556697 |
| Reference:
|
[7] Rosický, J., Tholen, W.: Factorization, fibration and torsion.Journal of Homotopy and Related Structures 355, no. 9, 3611–3623 MR 2369170 |
| . |
