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| \begin{corollary}(Corollary 1.4 in ref. \cite{BM266}) |
\begin{corollary}(Corollary 1.4 in ref. \cite{BM266})\\
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| Let $A$ be an object with a family of generators $\left\{A_i\right\}$ in a $C_3$-category. |
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 |
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 $A$. |
the $C_3$-category whose direct limit $\limdir \left\{A_i\right\}$ is $A$. |
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| \end{corollary} |
\end{corollary} |
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| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{BM266} |
\bibitem{BM266} |
| See p.83 in ref. $[266]$ in the |
See p.83 in ref. $[266]$ in the |
| \PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
\PMlinkname{Bibliography for categories and algebraic topology}{CategoricalOntologyABibliographyOfCategoryTheory} |
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| \end{thebibliography} |
\end{thebibliography} |
