Abstract
This paper presents a theory of uniform-type structures in the non-commutative sense. The theory comprises the theory of covering-uniformities for quantales as a generalization of the classical theory of covering-uniformities for frames. Also, by introducing quantale-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L a quantale). The categories of (covering) uniform quantales and L-valued uniform spaces here introduced and the adjunction between them is studied.
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