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A note on relations relative to a factorization system

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Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1488))

Abstract

A number of authors have observed that regularity of a category A is not necessary for the existence of a "calculus of relations" in A, with an associative composition of relations giving a 2-category Rel A; it suffices that the finitely-complete A have a proper factorization system (ε,M) whose class ε is stable by pullbacks, the classical regular-category case being that where M consists of all the monomorphisms. We show that this generalization is in a sense illusory: if B is the category of "maps" in Rel A, then B is a regular category, and Rel A is isomorphic to the classical Rel B.

The author acknowledges with gratitude the support of the Australian Research Council.

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Authors and Affiliations

  1. Pure Mathematics Department F07, University of Sydney, 2006, NSW, Australia

    G. M. Kelly

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  1. G. M. Kelly
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Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

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© 1991 Springer-Verlag

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Kelly, G.M. (1991). A note on relations relative to a factorization system. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084224

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  • DOI: https://doi.org/10.1007/BFb0084224

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

  • eBook Packages: Springer Book Archive

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