Publication detail

Free algebras in varieties

PAVLÍK, J.

Czech title

Volné algebry ve varietách

English title

Free algebras in varieties

Type

journal article - other

Language

en

Original 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.

Czech abstract

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.

English 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.

Keywords in Czech

kokompletní kategorie; volná algebra; varieta; přirozená transformace

Keywords in English

cocomplete category; free algebra; variety; natural transformation

RIV year

2010

Released

01.01.2010

Publisher

Masarykova univerzita

Location

Brno

ISSN

1212-5059

Journal

Archivum Mathematicum

Volume

46

Number

1

Pages from–to

25–38

Pages count

14

BIBTEX


@article{BUT49132,
  author="Jan {Pavlík},
  title="Free algebras in varieties",
  journal="Archivum Mathematicum",
  year="2010",
  volume="46",
  number="1",
  month="January",
  pages="25--38",
  publisher="Masarykova univerzita",
  address="Brno",
  issn="1212-5059"
}