$C_3$-category 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



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