Let $\mathcal A$ be an abelian category; $\mathcal B \subseteq \mathcal A$ a weak Serre subcategory. Does the inclusion $\mathbf D_{\mathcal B}(\mathcal A) \subseteq \mathbf D(\mathcal A)$ admit a left adjoint? If not in general, is there any condition on $\mathcal A$ and $\mathcal B$ that makes it true?
$\begingroup$
$\endgroup$
1
-
$\begingroup$ If $\mathbf D_{\mathcal B}(\mathcal A)$ is stable for coproducts in $\mathbf D(\mathcal A)$ and it has a set of generators, then the answer is yes. Is this what you need? $\endgroup$– Leo AlonsoCommented Feb 9, 2022 at 9:39
Add a comment
|