Chu connections and back diagonals between \(\mathcal{Q}\)-distributors. (English) Zbl 1338.18037
Summary: 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.
MSC:
| 18D20 | Enriched categories (over closed or monoidal categories) |
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |
| 06B23 | Complete lattices, completions |
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