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A Frith frame is a frame equipped with a join-dense bounded sublattice. In this talk we will see that Frith frames and suitable morphisms form a category Frith which is equivalent to the category of transitive and totally bounded quasi-uniform frames. This equivalence provides a very simple representation of transitive and totally bounded quasi-uniform frames. We will discuss some properties of Frith frames, paying special attention to the notion of completion inherited from the notion of completion of quasi-uniform frames. In particular, we will see that the category of coherent frames is, up to a natural identification, a full coreflective subcategory of Frith and that the completion of a Frith frame is precisely its coreflection. This is based on joint work with Anna Laura Suarez.
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