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[parent] $C_3$-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 ${\mathrm{\varinjlim}}\left\{A_i\right\}$ is $A$.

Bibliography

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



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This is version 3 of $C_3$-category generators corollary, born on 2010-05-09, modified 2010-05-09.
Object id is 859, canonical name is C_3CategoryGeneratorsCorollary.
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Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )
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