| Title:
|
Weakly globular double categories and weak units (English) |
| Author:
|
Paoli, Simona |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
269-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Weakly globular double categories are a model of weak 2-categories based on the notion of weak globularity, and they are known to be suitably equivalent to Tamsamani 2-categories. Fair 2-categories, introduced by J. Kock, model weak 2-categories with strictly associative compositions and weak unit laws. In this paper we establish a direct comparison between weakly globular double categories and fair 2-categories and prove they are equivalent after localisation with respect to the 2-equivalences. This comparison sheds new light on weakly globular double categories as encoding a strictly associative, though not strictly unital, composition, as well as the category of weak units via the weak globularity condition. (English) |
| Keyword:
|
higher categories |
| Keyword:
|
homotopy types |
| Keyword:
|
globular |
| Keyword:
|
double categories |
| MSC:
|
18D05 |
| MSC:
|
18G30 |
| idZBL:
|
Zbl 08141787 |
| idMR:
|
MR4918789 |
| DOI:
|
10.21136/HS.2025.06 |
| . |
| Date available:
|
2026-03-13T14:19:34Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153487 |
| . |
| Reference:
|
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| Reference:
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