Title:
|
Free algebras in varieties (English) |
Author:
|
Pavlík, Jan |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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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:
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free algebra |
Keyword:
|
variety |
Keyword:
|
natural transformation |
MSC:
|
08C05 |
MSC:
|
18C05 |
MSC:
|
18C20 |
idZBL:
|
Zbl 1240.08005 |
idMR:
|
MR2644452 |
. |
Date available:
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2010-04-22T10:41:52Z |
Last updated:
|
2013-09-19 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/139993 |
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Reference:
|
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Reference:
|
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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:
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Reference:
|
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Reference:
|
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Reference:
|
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Reference:
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