Publication detail

Varieties Defined without Colimits

PAVLÍK, J.

Czech title

Variety definované bez kolimit

English title

Varieties Defined without Colimits

Type

conference paper

Language

en

Original abstract

We define polymeric varieties of algebras for a functor as an analogy of varieties of functor algebras on a cocomplete category and we show that these concepts are compatible. Every variety induced by a set of identities is then proved to be concretely isomorphic to a polymeric variety for some functor. Using the result we obtain an alternative description of Eilenberg-Moore category for a free monad.

Czech abstract

Definujeme polymerické variety funktorových algeber jako analogie variet funktorových algeber na kokompletních kategoriích a ukazujeme, že tyto přístupy jsou rovnocenné. Dokazujeme, že každá varieta definována množinou identit je konkrétně izomorfní polymerické varietě algeber vhodného funktoru. Pomocí tohoto výsledku získáváme alternativní popis Eilenbergovy-Moorovy kategorie pro volnou monádu.

English abstract

We define polymeric varieties of algebras for a functor as an analogy of varieties of functor algebras on a cocomplete category and we show that these concepts are compatible. Every variety induced by a set of identities is then proved to be concretely isomorphic to a polymeric variety for some functor. Using the result we obtain an alternative description of Eilenberg-Moore category for a free monad.

Keywords in Czech

kategorie, funktorová algebra, varieta, přirozená transformace

Keywords in English

category, functor algebra, variety, natural transformation

RIV year

2009

Released

15.07.2009

Publisher

Patras University Press

Location

Patras, Řecko

ISBN

978-960-530-108-8

Book

Proceedings of the 7th Panhellenic Logic Symposium

Edition number

1

Pages from–to

142–146

Pages count

5

BIBTEX


@inproceedings{BUT31350,
  author="Jan {Pavlík},
  title="Varieties Defined without Colimits",
  booktitle="Proceedings of the 7th Panhellenic Logic Symposium",
  year="2009",
  month="July",
  pages="142--146",
  publisher="Patras University Press",
  address="Patras, Řecko",
  isbn="978-960-530-108-8"
}