CATEGORICAL STRUCTURES ENRICHED IN A QUANTALOID: CATEGORIES, DISTRIBUTORS AND FUNCTORS

We thoroughly treat several familiar and less familiar definitions and re- sults concerning categories, functors and distributors enriched in a base quantaloid Q.I n analogy with V-category theory we discuss such things as adjoint functors, (pointwise) left Kan extensions, weighted (co)limits, presheaves and free (co)completion, Cauchy completion and Morita equivalence. With an appendix on the universality of the quan- taloid Dist(Q )o fQ-enriched categories and distributors.

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