Fixed points in Cartesian closed categories (Q753945)

The author studies one aspect of domain theory in the setting of a cartesian closed category with finite limits and a natural numbers object. A notion of \(\omega\)-complete partial order in such a category is defined as well as notions of increasing sequences and an object of sup- preserving morphisms. There is shown that in such a setting an \(\omega\)- complete partial order with bottom has as fixed point operator in the sense of a mapping from the object of sup-preserving endomorphisms to the object itself that realizes the least fixed point.