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String diagrams for stably compact locales

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If you have a question about this talk, please contact Dr Steve Vickers.

NB This talk is at the theory seminar time (11.0 Friday) in the lab lunch room (217).

I continue my lab lunch talk from Thursday 27th, in which I introduced the entailment category Ent and described how -

(1) Ent is dual to the category of free frames and preframe homomorphisms.

(2)The Karoubi envelope Kar(Ent) is dual to the category of stably continuous frames and preframe homomorphisms.

Drew Moshier proposed that these categories, Ent and its Karoubi envelope, might get a string diagrammatic toolkit from structure as cartesian bicategories (Carboni and Walters – CW). This would provide strong analogies with Rel and its Karoubi envelope, which is equivalent to continuous dcpos and their Kleisli morphisms for the lower powerlocale.

Today I shall outline how this works for Ent. It is a cartesian bicategory. It is also compact closed, though not quite by the mechanism of “bicategories of relations”, proposed by CW, which applies to Rel.

This talk is part of the Lab Lunch series.

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