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Boundedness and Complete Distributivity

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Abstract

We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema. The KZ-doctrine for bounded suprema is of some independent interest and a few results about it are given. The 2-category of ordered sets admitting bounded suprema over which inhabited (classically non-empty) infima distribute is shown to be bi-equivalent to a 2-category defined in terms of idempotent relations. As a corollary we obtain a simple construction of the non-negative reals.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, E0A 3C0, Canada

    R. Rosebrugh

  2. Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, NS, B3H 3I5, Canada

    R. J. Wood

Authors
  1. R. Rosebrugh
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  2. R. J. Wood
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Rosebrugh, R., Wood, R.J. Boundedness and Complete Distributivity. Applied Categorical Structures 9, 437–456 (2001). https://doi.org/10.1023/A:1012095313842

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  • DOI: https://doi.org/10.1023/A:1012095313842

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