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Adjointness Aspects of the Down-Set Functor

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Abstract

The down-set construction, when applied to the category of Boolean frames, can be viewed as a functor into the category of frames with frame homomorphisms subject to various conditions akin to openness. We prove that it has a right adjoint, which is then given by Booleanization, exactly for near openness and one other, closely related property; a similar result is obtained for the finitary case of pseudocomplemented distributive lattices. In addition, we present a characterization of the frames which are down-set frames of Boolean frames.

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Authors and Affiliations

  1. MFF University Karlovy, Katedra Aplikovane Matem., Malostranske Nam. 25, 1180, Prague, Czech Republic

    B. Banaschewski & A. Pultr

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  1. B. Banaschewski
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  2. A. Pultr
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Banaschewski, B., Pultr, A. Adjointness Aspects of the Down-Set Functor. Applied Categorical Structures 9, 419–436 (2001). https://doi.org/10.1023/A:1011238428088

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