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Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)

Abstract:

It has been known since the work of Duskin and Pelletier four decades ago that Kop, the opposite of the category of compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that Kop is equivalent to a possibly infinitary variety of algebras Δ in the sense of Słomiński and Linton. Isbell showed in 1982 that the Lawvere–Linton algebraic theory of Δ can be generated using a finite number of finitary operations, together with a single operation of countably i...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.aim.2016.11.012

Authors


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Role:
Author
ORCID:
0000-0002-0727-4616
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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
ORCID:
0000-0001-7331-7381
Publisher:
Elsevier
Journal:
Advances in Mathematics More from this journal
Volume:
307
Pages:
253-287
Publication date:
2016-11-24
Acceptance date:
2016-11-14
DOI:
ISSN:
0001-8708

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