| Title:
|
Higher theories and monads (English) |
| Author:
|
Henry, Simon |
| Author:
|
Meadows, Nicholas J. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
227-268 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories and we use this to prove many classical results about monads in the $\infty$-categorical framework. Amongst other things, we show that the category of algebras for an accessible monad on a locally presentable $\infty$-category $\mathcal{E}$ is again locally presentable, and that a diagram of accessible monads on a locally presentable $\infty$-category admits a colimit. Our results also provide a new and simpler way to construct and describe monads in terms of theories. (English) |
| Keyword:
|
Monads |
| Keyword:
|
Theories |
| Keyword:
|
$\infty$-categories |
| Keyword:
|
Kleisli categories |
| MSC:
|
18C10 |
| MSC:
|
18C15 |
| MSC:
|
18N60 |
| MSC:
|
18N70 |
| idZBL:
|
Zbl 08141786 |
| idMR:
|
MR4918788 |
| DOI:
|
10.21136/HS.2025.05 |
| . |
| Date available:
|
2026-03-13T14:18:52Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153486 |
| . |
| Reference:
|
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