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}