| Title:
|
$(A_\infty,2)$-categories and relative 2-operads (English) |
| Author:
|
Bottman, Nathaniel |
| Author:
|
Carmeli, Shachar |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
5 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
401-421 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define the notion of a 2-operad relative to an operad, and prove that the 2-associahedra form a 2-operad relative to the associahedra. Using this structure, we define the notions of an $(A_\infty,2)$-category and $(A_\infty,2)$-algebra in spaces and in chain complexes over a ring. Finally, we show that for any continuous map $A \rightarrow X$, we can associate the related notion of an $\widetilde {(A_\infty,2)}$-algebra $\theta (A \rightarrow X)$ in Top, which specializes to $\theta (pt \rightarrow X)=\Omega^2 X$ and $\theta (A \rightarrow pt)=\Omega A \times \Omega A$. (English) |
| Keyword:
|
$(\infty,2)$-categories |
| Keyword:
|
higher operads |
| Keyword:
|
Fukaya categories |
| MSC:
|
18M60 |
| MSC:
|
18M75 |
| MSC:
|
18N10 |
| MSC:
|
18N65 |
| MSC:
|
53D37 |
| idZBL:
|
Zbl 1485.18027 |
| idMR:
|
MR4367226 |
| DOI:
|
10.21136/HS.2021.11 |
| . |
| Date available:
|
2026-03-13T05:39:51Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153443 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
