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Let $C$ be a Grothendieck category and $T$ a Serre subcategory of $C$. Let $\tilde{T}$ be the full subcategory of $C$ consisting of all direct limits of objects in $T$. DoesIs$\tilde{T}$ a Serre subcategory of $C$?
Any comment is welcome.
Let $C$ be a Grothendieck category and $T$ a Serre subcategory of $C$. Let $\tilde{T}$ be the full subcategory of $C$ consisting of all direct limits of objects in $T$. Does$\tilde{T}$ a Serre subcategory of $C$?
Any comment is welcome.
Let $C$ be a Grothendieck category and $T$ a Serre subcategory of $C$. Let $\tilde{T}$ be the full subcategory of $C$ consisting of all direct limits of objects in $T$. Is$\tilde{T}$ a Serre subcategory of $C$?
Let $C$ be a Grothendieck category and $T$ a Serre subcategory of $C$. Let $\tilde{T}$ be the full subcategory of $C$ consisting of all direct limits of objects in $T$. Does $\tilde{T}$ a Serre subcategory of $C$?
