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Grothendieck categories as quotient categories of $(R\mathrm{\text{-}mod},\mathrm{Ab})$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 983-992
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A Grothendieck category can be presented as a quotient category of the category $(R\mathrm{\text{-}mod},\mathrm{Ab})$ of generalized modules. In turn, this fact is deduced from the following theorem: if $\mathcal C$ is a Grothendieck category and there exists a finitely generated projective object $P\in\mathcal C$, then the quotient category $\mathcal C/\mathcal S^P$, $\mathcal S^P=\{C\in\mathcal C \mid{}_C(P,C)=0\}$ is equivalent to the module category $\mathrm{Mod\text{-}}R$, $R={}_C(P,P)$. 
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     author = {G. A. Garkusha and A. I. Generalov},
     title = {Grothendieck categories as quotient categories of $(R\mathrm{\text{-}mod},\mathrm{Ab})$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {983--992},
     year = {2001},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a1/}
}
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G. A. Garkusha; A. I. Generalov. Grothendieck categories as quotient categories of $(R\mathrm{\text{-}mod},\mathrm{Ab})$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 983-992. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a1/