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http://hdl.handle.net/10773/28975
Title: | Enriched Stone-type dualities |
Author: | Hofmann, Dirk Nora, Pedro |
Keywords: | Dual equivalence Quantale-enriched category Kleisli construction Vietoris functor Ordered compact Hausdorff space Metric compact Hausdorff space |
Issue Date: | 25-May-2018 |
Publisher: | Elsevier |
Abstract: | A common feature of many duality results is that the involved equivalence functors are liftings of hom-functors into the two-element space resp. lattice. Due to this fact, we can only expect dualities for categories cogenerated by the two-element set with an appropriate structure. A prime example of such a situation is Stone's duality theorem for Boolean algebras and Boolean spaces, the latter being precisely those compact Hausdorff spaces which are cogenerated by the two-element discrete space. In this paper we aim for a systematic way of extending this duality theorem to categories including all compact Hausdorff spaces. To achieve this goal, we combine duality theory and quantale-enriched category theory. Our main idea is that, when passing from the two-element discrete space to a cogenerator of the category of compact Hausdorff spaces, all other involved structures should be substituted by corresponding enriched versions. Accordingly, we work with the unit interval [0, 1] and present duality theory for ordered and metric compact Hausdorff spaces and (suitably defined) finitely cocomplete categories enriched in [0, 1]. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/28975 |
DOI: | 10.1016/j.aim.2018.03.010 |
ISSN: | 0001-8708 |
Appears in Collections: | CIDMA - Artigos AGG - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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stone_gelfand.pdf | 726.49 kB | Adobe PDF | View/Open |
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