algebra universalis

, Volume 14, Issue 1, pp 231–234 | Cite as

Free ω-complete algebras

  • Grzegorz Jarzembski
Article
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Abstract

In this paper we prove that for an arbitrary type Ω and an arbitrary strict ω-complete posetX the free ω-complete algebra of type Ω overX exists. Moreover, we prove, that for an arbitrary type (not necessary finitary!) this free algebra is, obtained by Adamek's construction in ω steps.

Keywords

Partial Order Free Algebra Forgetful Functor Bottom Element Unique Morphism 

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References

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    J. Adamek,Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae15 (1974) p. 589–602.MATHMathSciNetGoogle Scholar
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    M. Barr,Coequalizers and free triples. Math. Z116 (1970) p. 307–322.MATHMathSciNetCrossRefGoogle Scholar
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    J. A. Goguen, J. W. Thatcher, E. G. Wagner andJ. B. Wright,Some fundamentals of order-algebraic semantics, Lecture Notes in Comp. Sci.45 (1976) p. 153–168.MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • Grzegorz Jarzembski
    • 1
  1. 1.Nicholas Copemicus UniversityToruńPoland

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