Título: **
Cauchy Complete B**_{Q}-Categories

Autores: **
Joel Zamora
**

**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 B_{Q}-category, B_{Q}-functor,
B_{Q}-bimodule, and adjoint pairs of B_{Q}-bimodules;
and it is shown that Gelfand quantal sets and symmetric B_{Q}-categories
are equivalent concepts. In addition, it is shown that Gelfand maps of quantal
sets satisfying an extra condition and adjoint pairs of B_{Q}-bimodules
are also equivalent concepts. Finally, Cauchy-complete B_{Q}-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 B_{Q}-categories.

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