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$C_3$-category theorem (Theorem)
Theorem 0.1 (proposition 1.2. in ref. [1].)  

A cocomplete Abelian category is $C_3$ if and only if the direct limit of every direct family of subobjects $\left\{A_i\right\}$ of an object $A$ is equal to $\bigcup A_i$.

Bibliography

1
See p.82 and eq. (1) in ref. $[266]$ in the Bibliography for categories and algebraic topology



"$C_3$-category theorem" is owned by bci1.

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Other names:  Ab5 category, cocomplete Abelian category
Keywords:  cocomplete Abelian category, $C_3$ -category theorem

Attachments:
$C_3$-category corollary (Corollary) by bci1
$C_3$-category generators corollary (Corollary) by bci1

Cross-references: object, proposition
There are 2 references to this object.

This is version 2 of $C_3$-category theorem, born on 2010-05-09, modified 2010-05-09.
Object id is 857, canonical name is C_3CategoryTheorem.
Accessed 669 times total.

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 )
Pending Errata and Addenda
None.
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