2001/10/29 by Per Kristen Jakobsen, Per K. Jakobsen, Jakobsen, Per K. +2
Computer Science · Mathematics · #18B99 #81R99 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CT #math.QA #msc:18B99 #msc:81R99
paper · pdf · doi:10.48550/arxiv.math/0110311
corrected typos
openalex publication_date 2001/10/29 · arxiv created 2001/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.