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Journal of Logic and Computation 2002 12(2):217-242; doi:10.1093/logcom/12.2.217
© 2002 by Oxford University Press
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Original Article

Final Coalgebras are Ideal Completions of Initial Algebras

Jirí Adámek1

1 Technical University of Braunschweig, Postfach 3329, 38106 Braunschweig, Germany. E-mail: J.Adamek{at}tu-bs.de

For {omega}-continuous endofunctors of Set an ordering of a final coalgebra T is exhibited which makes T a CPO. Moreover, an initial algebra, considered as a canonical subobject of T, hasT as its ideal completion. In more generality, for {omega}-continuous endofunctors of locally finitely presentable categories the analogous result holds: here the ordering is considered on the hom-sets hom(B, T) for all finitely presentable objects B.

Keywords: Final coalgebra; initial algebra; complete partial order; ideal completion; algebraically complete; locally presentable category

Received September 2000.


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