# PlanetPhysics/C 3CategoryGeneratorsCorollary

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}

\begin{corollary}(Corollary 1.4 in ref.^{[1]})

Let be an object with a family of generators in a -category.
Then, the finitely generated subobjects of form a direct family of subobjects in
the -category whose direct limit **Failed to parse (unknown function "\limdir"): {\displaystyle \limdir \left\{A_i\right\}}**
is .

\end{corollary}

## All SourcesEdit

^{[1]}

## ReferencesEdit

- ↑
^{1.0}^{1.1}See p.83 in ref. in the Bibliography for categories and algebraic topology