| Title:
|
A remark on accessible and axiomatizable categories (English) |
| Author:
|
Adámek, Jiří |
| Author:
|
Rosický, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
411-414 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle. (English) |
| Keyword:
|
accessible category |
| Keyword:
|
infinitary logic |
| Keyword:
|
Vopěnka's principle |
| MSC:
|
03C99 |
| MSC:
|
18B99 |
| idZBL:
|
Zbl 0849.18005 |
| idMR:
|
MR1399015 |
| . |
| Date available:
|
2009-01-08T18:24:49Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118845 |
| . |
| Reference:
|
[AR] Adámek J., Rosický J.: Locally Presentable and Accessible Categories.Cambridge Univ. Press, 1994. MR 1294136 |
| Reference:
|
[D] Diers Y.: Catégories localement multiprésentables.Arch. Math. 34 (1980), 344-356. Zbl 0453.18002, MR 0593951 |
| Reference:
|
[F] Fisher E.R.: Vopěnka's principle, category theory and universal algebra.personal communication, 1987. |
| Reference:
|
[J] Jech T.: Set Theory.Academic Press, 1978. Zbl 1007.03002, MR 0506523 |
| Reference:
|
[L] Lair C.: Catégories modélables et catégories esquissables.Diagrammes 6 (1981), 1-20. Zbl 0522.18008, MR 0684535 |
| Reference:
|
[MP] Makkai M., Paré R.: Accessible categories: the foundations of categorical model theory.Contemp. Math. 104 (1989). MR 1031717 |
| Reference:
|
[RTA] Rosický J., Trnková V., Adámek J.: Unexpected properties of locally presentable categories.Alg. Univ. 27 (1990), 153-170. MR 1037859 |
| . |
