Abstract
For ω‐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 ω‐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.
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