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http://hdl.handle.net/10773/28975
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DC Field | Value | Language |
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dc.contributor.author | Hofmann, Dirk | pt_PT |
dc.contributor.author | Nora, Pedro | pt_PT |
dc.date.accessioned | 2020-07-30T18:11:08Z | - |
dc.date.available | 2020-07-30T18:11:08Z | - |
dc.date.issued | 2018-05-25 | - |
dc.identifier.issn | 0001-8708 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/28975 | - |
dc.description.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]. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Elsevier | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/5876/147206/PT | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/SFRH/SFRH%2FBD%2F95757%2F2013/PT | pt_PT |
dc.rights | openAccess | pt_PT |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | pt_PT |
dc.subject | Dual equivalence | pt_PT |
dc.subject | Quantale-enriched category | pt_PT |
dc.subject | Kleisli construction | pt_PT |
dc.subject | Vietoris functor | pt_PT |
dc.subject | Ordered compact Hausdorff space | pt_PT |
dc.subject | Metric compact Hausdorff space | pt_PT |
dc.title | Enriched Stone-type dualities | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.firstPage | 307 | pt_PT |
degois.publication.lastPage | 360 | pt_PT |
degois.publication.title | Advances in Mathematics | pt_PT |
degois.publication.volume | 330 | pt_PT |
dc.identifier.doi | 10.1016/j.aim.2018.03.010 | pt_PT |
dc.identifier.essn | 1090-2082 | pt_PT |
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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