Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)
Vincenzo Marra; Luca Reggio · 2015 · arXiv
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Abstract (excerpt)
It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a possibly infinitary variety of algebras V in the sense of Slominski and Linton. Isbell showed in 1982 that the Lawvere-Linton algebraic theory of V can be generated using a finite number of finitary operations, together with a single operation of countably infinite arity. In 1983, Banaschewski and Rosicky independently proved a conjecture of Bankston, establishi
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Metadata source: arXiv