PAVLÍK, Jan. Free algebras in varieties. Archivum Mathematicum, Brno. Brno: Masarykova univerzita, 2010, 1/2010, No 2010, p. 25-38. ISSN 0044-8753.
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Basic information
Original name Free algebras in varieties
Name in Czech Volné algebry ve varietách
Name (in English) Free algebras in varieties
Authors PAVLÍK, Jan.
Edition Archivum Mathematicum, Brno, Brno, Masarykova univerzita, 2010, 0044-8753.
Other information
Type of outcome Article in a journal
Confidentiality degree is not subject to a state or trade secret
Organization unit Faculty of Science
Keywords (in Czech) kokompletní kategorie; volná algebra; varieta; přirozená transformace
Keywords in English cocomplete category; free algebra; variety; natural transformation
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Changed by Changed by: Mgr. Jan Pavlík, Ph.D., učo 23428. Changed: 1. 3. 2012 12:20.
Abstract
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.
Abstract (in Czech)
Pomocí dvojic přirozených transformací definujeme variety algeber pro libovolný endofunktor na kokompletní kategorii. Je tu dokázáno, že tento přístup je rovnocenný s popisem pomocí rovnicových šipek. Studujeme volné algebry ve varietách je dokázána jejich existence za předpokladů dosažitelnosti identit.
Abstract (in English)
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.
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