PlanetPhysics/C 3CategoryTheorem

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\begin{theorem} (proposition 1.2. in ref. .)

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 $\bigcup A_{i}$. \end{theorem}