| Title:
|
Colimit-dense subcategories (English) |
| Author:
|
Adámek, Jiří |
| Author:
|
Brooke-Taylor, Andrew D. |
| Author:
|
Campion, Tim |
| Author:
|
Positselski, Leonid |
| Author:
|
Rosický, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
447-462 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vopěnka's Principle, we prove that a cocomplete category is locally presentable if and only if it has a colimit dense subcategory and a generator consisting of presentable objects. We further show that a $3$-element set is colimit-dense in ${\mathbf{Set}}^{\rm op}$, and spaces of countable dimension are colimit-dense in ${\mathbf{Vec}}^{\rm op}$. (English) |
| Keyword:
|
locally presentable category |
| Keyword:
|
colimit-dense subcategory |
| Keyword:
|
Vopěnka's Principle |
| MSC:
|
03E55 |
| MSC:
|
18A30 |
| MSC:
|
18C35 |
| idZBL:
|
Zbl 07177882 |
| idMR:
|
MR4061355 |
| DOI:
|
10.14712/1213-7243.2019.021 |
| . |
| Date available:
|
2020-02-10T16:48:15Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147976 |
| . |
| Reference:
|
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| . |
