| Title:
|
Fibrations of $\infty$-categories (English) |
| Author:
|
Ayala, David |
| Author:
|
Francis, John |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
4 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
168-265 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a flagged $\infty$-category $\bf Corr$ of $\infty$-categories and bimodules among them. We prove that $\bf Corr$ classifies exponentiable fibrations. This representability of exponentiable fibrations extends that established by Lurie of both coCartesian fibrations and Cartesian fibrations, as they are classified by the $\infty$-category of $\infty$-categories and its opposite, respectively. We introduce the flagged $\infty$-subcategories $\bf LCorr$ and $\bf RCorr$ of $\bf Corr$, whose morphisms are those bimodules which are {\it left-final} and {\it right-initial}, respectively. We identify the notions of fibrations these flagged $\infty$-subcategories classify, and show that these $\infty$-categories carry universal left/right fibrations. (English) |
| Keyword:
|
Infinity categories |
| Keyword:
|
Exponentiable fibrations |
| Keyword:
|
Cartesian and coCartesian fibrations |
| Keyword:
|
Correspondences |
| Keyword:
|
Segal spaces |
| Keyword:
|
Final functors |
| Keyword:
|
Initial functors |
| MSC:
|
18A22 |
| MSC:
|
55P65 |
| MSC:
|
55U35 |
| idZBL:
|
Zbl 1440.18003 |
| idMR:
|
MR4074276 |
| DOI:
|
10.21136/HS.2020.05 |
| . |
| Date available:
|
2026-03-11T21:20:14Z |
| Last updated:
|
2026-03-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153420 |
| . |
| Reference:
|
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