The categorical theory of relations and quantization

The categorical theory of relations and quantization

In this paper we develops 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...

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Hauptverfasser: Lychagin, Valentin V, Jakobsen, Per K
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Sprache:eng
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Algebra/algebraic analysis: 414
Mathematics and natural science: 400
Mathematics: 410
VDP
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Jakobsen, Per K
description In this paper we develops 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.
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subjects Algebra/algebraic analysis: 414
Mathematics and natural science: 400
Mathematics: 410
VDP
title The categorical theory of relations and quantization
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