QUANTALOIDS AND SHEAVES ON RIGHT GELFAND QUANTALES
A quantale is a semigroup in SUP. A right Gelfand quantale is a complete lattice equipped with an associative binary operation & (possibly non-commutative) which is idempotent, has right identity and distributes over arbitrary suprema on both sides. A quantaloid is a SUP-enriched category. In this paper we obtain a quantaloid from a right Gelfand quantale. We also discuss two approaches for introduction of concept of sheaf on a right Gelfand quantale Q. In both cases the construction coincides with the concept of sheaf in case Q is a locale.