PlanetPhysics/C 3CategoryGeneratorsCorollary

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\begin{corollary}(Corollary 1.4 in ref. )

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 $$\limdir \left\{A_i\right\}$$ is $$A$$.

\end{corollary}