Categories of Fractions
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 35)
A functor F: L→D 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
L a category L[Σ−1] and a functor P Σ : L→L[Σ−1] such that the following conditions are verified:
P Σ makes the morphisms of Σ invertible,
If a functor F: L→X 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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© Springer-Verlag Berlin · Heidelberg 1967