Categories of Fractions

  • Peter Gabriel
  • Michel Zisman
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 35)

Abstract

A functor F: LD is said make a morphism σ of L invertible if Fσ is invertible. We intend to associate with each category L and with each subset Σ of
$$\mathfrak{A}r$$
L a category L[Σ−1] and a functor P Σ : LL[Σ−1] such that the following conditions are verified:
  1. (i)

    P Σ makes the morphisms of Σ invertible,

     
  2. (ii)

    If a functor F: LX makes the morphisms of Σ invertible, there exists one and only one functor G: L[Σ−1]→X such that F=G·P Σ .

     

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1967

Authors and Affiliations

  • Peter Gabriel
    • 1
  • Michel Zisman
    • 1
  1. 1.Departement de Mathématique StrasbourgUniversité de StrasbourgFrance

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