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'local Grothendieck category'
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| Title of object: |
local Grothendieck category |
| Canonical Name: |
LocalGrothendieckCategory |
| Type: |
Definition |
| Created on: |
2008-07-13 01:02:25 |
| Modified on: |
2008-07-15 11:33:14 |
| Classification: |
msc:18E05 |
| Keywords: |
Alexander Grothendieck, local Grothendieck category |
| Defines: |
local Grothendieck category |
| Synonyms: |
local Grothendieck category=Abelian category |
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Content:
\textbf{Definition 01:} A {\em local Grothendieck category} is a Grothendieck category
$\mathcal{\G}$ with a simple object S whose injective envelope $E(S)$ is
a cogenerator of $\mathcal{\G}$; cf. N. Popescu: p. 295 in {\em "Abelian Categories with Applications to Rings and Modules"}, Academic Press: New York and London, 1973, 1976, ({\em English translation by I. C. Baianu}). |
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