The categorical theory of relations and quantizations

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dc.creatorJakobsen, Per K.
dc.creatorLychagin, Valentin
dc.date2001-10-29
dc.date2001-10-30
dc.date.accessioned2026-07-07T04:44:08Z
dc.date.available2026-07-07T04:44:08Z
dc.descriptionIn this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of $A-A$ bicomodules. Properties of relations are defined in terms of the symmetric monoidal structure. Equivalence relations are shown to be commutative monoids in the category of relations. Quantization in our view is a property of functors between monoidal categories. This notion of quantization induce a deformation of all algebraic structures in the category, in particular the ones defining properties of relations like transitivity and symmetry.
dc.descriptioncorrected typos
dc.identifierhttps://arxiv.org/abs/math/0110311
dc.identifierhttp://arxiv.org/abs/math/0110311
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62514
dc.subjectQuantum Algebra
dc.subjectCategory Theory
dc.subject18B99, 81R99
dc.titleThe categorical theory of relations and quantizations
dc.typetext

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