Cauchy Complete BQ-Categories

• Autores: Joel Zamora
• Localización: Foro-Red-Mat: Revista electrónica de contenido matemático, ISSN 1405-1745, Vol. 28, Nº. 5, 2011
• Idioma: inglés
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• Resumen

  • Following the ideas of Lawvere and Walters, is constructed in this paper a bicategory from a locally Gelfand quantale Q. Then are studied the concepts of BQ-category, BQ-functor, BQ-bimodule, and adjoint pairs of BQ-bimodules; and it is shown that Gelfand quantal sets and symmetric BQ-categories are equivalent concepts. In addition, it is shown that Gelfand maps of quantal sets satisfying an extra condition and adjoint pairs of BQ-bimodules are also equivalent concepts. Finally, Cauchy-complete BQ-categories are studied and it is shown that there exists an isomorphism between a subcategory of the category of Complete Q-Sets and the category of symmetric skeletal Cauchy complete BQ-categories.