Free algebras in varieties

PAVLÍK, Jan. Free algebras in varieties. Archivum Mathematicum, Brno. Brno: Masarykova univerzita, 2010, 1/2010, No 2010, p. 25-38. ISSN 0044-8753.

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
• Tags: Reviewed

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.