| Title:
|
Free algebras in varieties (English) |
| Author:
|
Pavlík, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
25-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility. (English) |
| Keyword:
|
cocomplete category |
| Keyword:
|
free algebra |
| Keyword:
|
variety |
| Keyword:
|
natural transformation |
| MSC:
|
08C05 |
| MSC:
|
18C05 |
| MSC:
|
18C20 |
| idZBL:
|
Zbl 1240.08005 |
| idMR:
|
MR2644452 |
| . |
| Date available:
|
2010-04-22T10:41:52Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/139993 |
| . |
| Reference:
|
[1] Adámek, J.: Free algebras and automata realizations in the language of categories.Comment. Math. Univ. Carolin. 015 (4) (1974), 589–602. MR 0352209 |
| Reference:
|
[2] Adámek, J., Herrlich, H., Strecker, G. E.: Abstract and concrete categories.Free Software Foundation, 1990/2006. MR 1051419 |
| Reference:
|
[3] Adámek, J., Porst, H.: From varieties of algebras to covarieties of coalgebras.Math. Structures Comput. Sci. (2001). Zbl 1260.08004 |
| Reference:
|
[4] Adámek, J., Rosický, J.: Locally presentable and accessible categories.Cambridge University Press, 1994. MR 1294136 |
| Reference:
|
[5] Adámek, J., Trnková, V.: Birkhoff’s variety theorem with and without free algebras.Theory Appl. Categ. 14 (18) (2005), 424–450. Zbl 1086.18003, MR 2211426 |
| Reference:
|
[6] Barr, M.: Coequalizers and free triples.Math. Z. 116 (1970), 307–322. Zbl 0194.01701, MR 0272849, 10.1007/BF01111838 |
| Reference:
|
[7] Kelly, G. M.: A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on.Bull. Austral. Math. Soc. 22 (1) (1980), 1–83. Zbl 0437.18004, MR 0589937, 10.1017/S0004972700006353 |
| Reference:
|
[8] MacLane, S.: Categories for the working mathematician.Springer-Verlag, 1971. MR 0354798 |
| Reference:
|
[9] Reiterman, J.: One more categorical model of universal algebra.Math. Z. 161 (2) (1978), 137–146. Zbl 0363.18007, MR 0498325, 10.1007/BF01214925 |
| Reference:
|
[10] Reiterman, J.: On locally small based algebraic theories.Comment. Math. Univ. Carolin. 27 (2) (1986), 325–340. Zbl 0598.18003, MR 0857552 |
| . |
