PlanetPhysics/C 3CategoryGeneratorsCorollary

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

Let $A$ be an [[../TrivialGroupoid/|object]] with a family of [[../Generator/|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 Failed to parse (unknown function "\limdir"): {\displaystyle \limdir \left\{A_i\right\}} is $A$.

\end{corollary}