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Version 15 |
| \begin{definition} A \emph{local Grothendieck category} is a \emph{Grothendieck category} |
\begin{definition} A \emph{local Grothendieck category} is a \emph{Grothendieck category} |
| $\mathcal{\G}$ with a simple object $S$ whose injective envelope $E(S)$ is |
$\mathcal{\G}$ with a simple object $S$ whose injective envelope $E(S)$ is |
| a cogenerator of $\mathcal{\G}$; viz. \cite{NP75}. |
a cogenerator of $\mathcal{\G}$; viz. \cite{NP75}. |
| \end{definition} |
\end{definition} |
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| {\bf Note:} |
{\bf Note:} |
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This is related and attached to the entry on the \emph{Grothendieck category}; thus, it is also relevant to
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This is related and attached to the entry on \emph{Grothendieck category}; thus, it is also relevant to
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| \PMlinkname{Abelian categories}{AlternativeDefinitionOfAnAbelianCategory}. |
\PMlinkname{Abelian categories}{AlternativeDefinitionOfAnAbelianCategory}. |
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| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{NP75} |
\bibitem{NP75} |
| N. Popescu: \emph{Abelian Categories with Applications to Rings and Modules}, Academic Press: New York and London, 1973, 1975 2nd edn, p. 295 (\emph{English translation by I. C. Baianu}) |
N. Popescu: \emph{Abelian Categories with Applications to Rings and Modules}, Academic Press: New York and London, 1973, 1975 2nd edn, p. 295 (\emph{English translation by I. C. Baianu}) |
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| \end{thebibliography} |
\end{thebibliography} |
