FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 4, PAGES 983-992
G. A. Garkusha
A. I. Generalov
Abstract
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A Grothendieck category can be presented
as a quotient category of the category
$(R\mathrm{-mod}, \mathrm{Ab})$
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
$\mathrm{Mod-}R$ ,
$R = {}_C (P,P)$ .
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Last modified: April 17, 2002