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algebra universalis

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

Free ω-complete algebras

  • Grzegorz Jarzembski
Article
  • 21 Downloads

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J. Adamek,Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae15 (1974) p. 589–602.MATHMathSciNetGoogle Scholar
  2. [2]
    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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