PlanetMath: $C_3$-category generators corollary

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-category generators corollary

(Corollary)

Corollary 0.1 (Corollary 1.4 in ref. [1])

Let $A$ be an object with a family of generators $\left\{A_i\right\}$ in a $C_3$ -category. Then, the finitely generated subobjects of $A$ form a direct family of subobjects in the $C_3$ -category whose direct limit $\limdir \left\{A_i\right\}$ is $A$ .

Bibliography

1: See p.83 in ref. $[266]$ in the Bibliography for categories and algebraic topology

-category generators corollary" is owned by bci1.

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-category, generators corollary

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-category generators corollary, born on 2008-09-27, modified 2009-01-12.
Object id is 11100, canonical name is C_3CategoryGeneratorsCorollary.
Accessed 438 times total.

Classification:

AMS MSC:	18E15 (Category theory; homological algebra :: Abelian categories :: Grothendieck categories)
	18E10 (Category theory; homological algebra :: Abelian categories :: Exact categories, abelian categories)
	18-00 (Category theory; homological algebra :: General reference works )
	18A99 (Category theory; homological algebra :: General theory of categories and functors :: Miscellaneous)

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