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Journal of Logic and Computation

Volume 12, Issue 2, April 2002: pp. 217-242

Final Coalgebras are Ideal Completions of Initial Algebras

Ji[rcaron]í Adámek1

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

For [ohgr]-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 [ohgr]-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

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