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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikiversity.org/v1/":): {\displaystyle \limdir \left\{A_i\right\}} is $A$.

\end{corollary}