$C_3$-category generators corollary

Corollary 0.1 (Corollary 1.4 in ref. [1])  

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 $ {\mathrm{\varinjlim}}\left\{A_i\right\}$ is $ A$ .

Bibliography

1
See p.83 in ref. $ [266]$ in the Bibliography for categories and algebraic topology



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