Geodesic
Categorical structures enriched in a quantaloid: categories, distributors and functors
Theory and applications of categories, Tome 14 (2005), pp. 1-45

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We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In 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 quantaloid Dist(Q) of Q-enriched categories and distributors.

Classification : 06F07, 18B35, 18D20
Keywords: Quantales and quantaloids, enriched categories 
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     title = {Categorical structures enriched in a quantaloid: categories, distributors and functors},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2005_14_a0/}
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Isar Stubbe. Categorical structures enriched in a quantaloid: categories, distributors and functors. Theory and applications of categories, Tome 14 (2005), pp. 1-45. http://geodesic.mathdoc.fr/item/TAC_2005_14_a0/