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Note on free algebras over continuous domains. (English) Zbl 0896.08008
Summary: We provide a simple direct proof that for a finitary signature and a set of inequalities the free algebra functor on the category of directed complete partial orders (dcpo’s) takes continuous, respectively algebraic, dcpo’s to free algebras whose underlying dcpo is again continuous, respectively algebraic.

MSC:
08B20 Free algebras
06B35 Continuous lattices and posets, applications
68Q55 Semantics in the theory of computing
08A70 Applications of universal algebra in computer science
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References:
[1] Abramsky, S.; Jung, A., Domain theory, (), 1-168
[2] Hoffmann, R.-E., Continuous posets and adjoint sequences, (), 173-188 · Zbl 0427.06003
[3] Kock, A., Monads for which structures are adjoint to units, (June 1993), preprint
[4] Nelson, E., Gne; -continuous algebras, (), 315-334, Bremen, FRG
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