Many-valued complete distributivity

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dc.creatorLai, Hongliang
dc.creatorZhang, Dexue
dc.date2006-03-25
dc.date2006-05-12
dc.date.accessioned2026-07-07T07:07:13Z
dc.date.available2026-07-07T07:07:13Z
dc.descriptionCategories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulated in the many-valued setting in terms of categorical postulations. So, it is possible, by aid of categorical machineries, to establish theories of many-valued complete lattices, many-valued completely distributive lattices, and so on. This paper presents a systematical investigation of many-valued complete distributivity, including the topics: (1) subalgebras and quotient algebras of many-valued completely distributive lattices; (2) categories of (left adjoint) functors; and (3) the relationship between many-valued complete distributivity and properties of the quantale of truth values. The results show that enriched category theory is a very useful tool in the study of many-valued versions of order-related mathematical entities.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math/0603590
dc.identifierhttp://arxiv.org/abs/math/0603590
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110309
dc.subjectCategory Theory
dc.subjectLogic
dc.subject03G25,06D10,06F07,18B35,18D20,68Q55
dc.titleMany-valued complete distributivity
dc.typetext

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