| Title:
|
Weakly invertible cells in a weak $\omega$-category (English) |
| Author:
|
Fujii, Soichiro |
| Author:
|
Hoshino, Keisuke |
| Author:
|
Maehara, Yuki |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
8 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
386-415 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study weakly invertible cells in weak $\omega$-categories in the sense of Batanin–Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $\omega$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $\omega$-categories to weak $\omega$-categories, and show that every weak $\omega$-category has a largest weak $\omega$-subgroupoid. (English) |
| Keyword:
|
Weak $\omega$-category |
| Keyword:
|
weak $\omega$-groupoid |
| Keyword:
|
weakly invertible cell |
| Keyword:
|
equivalence |
| MSC:
|
18N20 |
| MSC:
|
18N65 |
| idZBL:
|
Zbl 1558.18022 |
| idMR:
|
MR4835393 |
| DOI:
|
10.21136/HS.2024.14 |
| . |
| Date available:
|
2026-03-13T14:39:38Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153479 |
| . |
| Reference:
|
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| Reference:
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