PlanetPhysics/C 3CategoryGeneratorsCorollary

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

\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 Failed to parse (unknown function "\limdir"): {\displaystyle \limdir \left\{A_i\right\}} is $A$.

\end{corollary}