| Title:
|
On flat covers in varieties (English) |
| Author:
|
Kruml, David |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
19-24 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers. (English) |
| Keyword:
|
flat object |
| Keyword:
|
flat cover |
| Keyword:
|
variety |
| Keyword:
|
cosimplicial object |
| MSC:
|
16D40 |
| MSC:
|
18G05 |
| MSC:
|
18G30 |
| idZBL:
|
Zbl 1212.18014 |
| idMR:
|
MR2432817 |
| . |
| Date available:
|
2009-05-05T17:06:11Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119698 |
| . |
| Reference:
|
[1] Adámek J., Rosický J.: Locally Presentable and Accessible Categories.Cambridge University Press, Cambridge, 1994. MR 1294136 |
| Reference:
|
[2] Bican L., El Bashir R., Enochs E.: All modules have flat cover.Bull. London Math. Soc. 33 (2001), 45-51. MR 1832549, 10.1017/S0024609301008104 |
| Reference:
|
[3] Borceux F., Rosický J.: On von Neumann varieties.Theory Appl. Categ. 13 (2004), 5-26. Zbl 1057.18004, MR 2116320 |
| Reference:
|
[4] Borceux F., Rosický J.: Purity in algebra.Algebra Universalis 56 (2007), 17-35. Zbl 1116.08004, MR 2280436, 10.1007/s00012-006-1977-x |
| Reference:
|
[5] Johnstone P.T.: Affine categories and naturally Malcev categories.J. Pure Appl. Algebra 61 (1989), 251-256. MR 1027744, 10.1016/0022-4049(89)90075-3 |
| Reference:
|
[6] Kilp M., Knauer U., Mikhalev A.V.: Monoids, Acts and Categories.Walter de Gruyter, New York, 2000. Zbl 0945.20036, MR 1751666 |
| Reference:
|
[7] Rosický J.: Flat covers and factorizations.J. Algebra 263 (2002), 1-13. Zbl 1024.18002, MR 1925005, 10.1016/S0021-8693(02)00043-1 |
| Reference:
|
[8] Rosický J.: On projectivity in locally presentable categories.J. Algebra 272 (2004), 701-710. Zbl 1040.18008, MR 2028077, 10.1016/j.jalgebra.2003.09.014 |
| . |
