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Chu connections and back diagonals between $mathcal{Q}$-distributors

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 نشر من قبل Lili Shen
 تاريخ النشر 2015
  مجال البحث الهندسة المعلوماتية
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Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid $mathcal{Q}$. These notions, meaningful for closed bicategories, dualize the constructions of arrow categories and the Freyd completion of categories. It is shown that, for a small quantaloid $mathcal{Q}$, the category of complete $mathcal{Q}$-categories and left adjoints is a retract of the dual of the category of $mathcal{Q}$-distributors and Chu connections, and it is dually equivalent to the category of $mathcal{Q}$-distributors and back diagonals. As an application of Chu connections, a postulation of the intuitive idea of reduction of formal contexts in the theory of formal concept analysis is presented, and a characterization of reducts of formal contexts is obtained.



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