Geodesic
A Note on the Universe of a Category of Fractions
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 425-427

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Let be a small -category where is a fixed Grothendieck universe, i.e., the objects of form a set which is a subset of and, for every pair of objects X, Y of the set is an element of . If S is a set of morphisms of , then, in general, the category of fractions [S- 1] would belong to a higher universe ([4], p. 256). 
Nanda, Sribatsa. A Note on the Universe of a Category of Fractions. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 425-427. doi: 10.4153/CMB-1980-062-9
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