Fixed points in cartesian closed categories

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The purpose of this paper is to begin the study of domain theory in a context that is also appropriate for semantic models of other aspects of computation, that is in cartesian closed categories with a natural numbers object. I show that if D is an internally ω-complete partial order with bottom in such a category, then the usual construction of least fixed point of an ω-continuous endomorphism can be internalized as an arrow from the object of ω-continuous endomorphisms of D (suitably defined) to D itself. © 1990.




Barr, M. (1990). Fixed points in cartesian closed categories. Theoretical Computer Science, 70(1), 65–72.

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