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local Grothendieck category

(Definition)

Definition 0.1 A local Grothendieck category is a Grothendieck category $\mathcal{\G}$ with a simple object $S$ whose injective envelope $E(S)$ is a cogenerator of $\mathcal{\G}$ ; viz. [1].

Note:

This is related and attached to the entry on the Grothendieck category; thus, it is also relevant to Abelian categories.

Bibliography

1: N. Popescu: Abelian Categories with Applications to Rings and Modules, Academic Press: New York and London, 1973, 1975 2nd edn, p. 295 (English translation by I. C. Baianu)

"local Grothendieck category" is owned by bci1.

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Other names:

Abelian category

Also defines:

local category

Keywords:

Alexander Grothendieck, local Grothendieck category

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Cross-references: viz, cogenerator, injective envelope, object, simple, Grothendieck category
There are 3 references to this entry.

This is version 16 of local Grothendieck category, born on 2008-07-13, modified 2009-02-01.
Object id is 10780, canonical name is LocalGrothendieckCategory.
Accessed 1228 times total.

Classification:

18E05 (Category theory; homological algebra :: Abelian categories :: Preadditive, additive categories)

Pending Errata and Addenda

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