| Title:
|
Discrete 2-Fibrations (English) |
| Author:
|
Lambert, Michael |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
8 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
54-96 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is a study of 2-dimensional discrete fibrations. A definition is proposed as a specialization of 2-fibrations. It is shown that discrete 2-fibrations correspond via a category of elements construction to contravariant category-valued 2-functors. The second part of the paper is dedicated to a monadicity result. It is shown that 2-fibrations are algebras for a monad given by an action of Bénabou’s cylinders construction. This should be seen as categorifying the monad for which ordinary fibrations are algebras, namely, that given by an action of an ordinary arrow category. Monadicity of discrete 2-fibrations is recovered by restricting the cylinders monad. To support the correctness of this categorification, it is shown that cylinders are a cotensor in a 3-categorical structure of 2-categories, 2-functors, lax natural transformations and modifications. This is an example of a lax 3-category which is introduced here to describe this universality. (English) |
| Keyword:
|
Discrete Fibrations |
| Keyword:
|
2-Fibrations |
| Keyword:
|
Monadicity |
| Keyword:
|
Lax Transformations |
| MSC:
|
18D05 |
| MSC:
|
18D30 |
| idZBL:
|
Zbl 1547.18011 |
| idMR:
|
MR4752518 |
| DOI:
|
10.21136/HS.2024.02 |
| . |
| Date available:
|
2026-03-13T14:05:08Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153466 |
| . |
| Reference:
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