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4 votes

Is an abelian category a Serre subcategory of its ind-category?

(1) is proved in Kashiwara-Schapira [KS], Theorem 8.6.5. For (2), [KS], Proposition 8.6.11 prove that $\mathcal C$ is closed under kernels, cokernels, and extensions in $Ind(\mathcal C)$. I believe th …
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