A category of fractions is a localization that is constructed using a calculus of fractions.
For a generalisation, see bicategory of fractions.
Pierre Gabriel, Michel Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer (1967) (pdf)
Frank Adams, part III, section 14 of Stable homotopy and generalised homology, 1974
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