Abstract
In this chapter we will prove that every quotient category Mod-(A, ℑ) is a Grothendieck category. The proof uses arguments of a rather general nature, and it can also be used to show that the category of abelian sheaves on a topological space is a Grothendieck category. The second main result of this chapter is the Popescu-Gabriel theorem, which states that every Grothendieck category actually is a quotient category of a module category.
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© 1975 Springer-Verlag Berlin Heidelberg
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Stenström, B. (1975). The Category of Modules of Quotients. In: Rings of Quotients. Die Grundlehren der mathematischen Wissenschaften, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66066-5_12
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DOI: https://doi.org/10.1007/978-3-642-66066-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66068-9
Online ISBN: 978-3-642-66066-5
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