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A note on relations relative to a factorization system

Part I

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Factorization System
  • Short Exact Sequence
  • Full Subcategory
  • Left Adjoint
  • Separate Object

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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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

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