Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories

Details Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories

2004-09-24

arxiv.org/abs/math/0409475v1

Mathematics

Category Theory

21 pages

Scientific paper

We study presheaves on semicategories enriched in a quantaloid: this gives rise to the notion of regular presheaf. A semicategory is regular when its representable presheaves are regular, and its regular presheaves then constitute an essential (co)localization of the category of all of its presheaves. The notion of regular semidistributor allows to establish the Morita equivalence of regular semicategories. Continuous orders and Omega-sets provide examples.

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