Let $R$ be an unital ring and consider the category of left $R$-modules $R$-Mod. We call a full subcategory $\mathcal{W}\subset R$-Mod a localizing Serre subcategory if $\mathcal{W}$ is closed under isomorphisms, subobjects, quotients, extensions and coproducts. On the other hand, for an arbitrary class of objects $\mathcal{S}\subset R$-Mod, we could define its left and right orthogonals as the full subcategories $$ ^{\bot}\mathcal{S}:\{X|\text{Ext}^i(X,S)=0, \forall S\in \mathcal{S},\forall i\geq 0\} $$ and $$ \mathcal{S}^{\bot}:\{X|\text{Ext}^i(S,X)=0, \forall S\in \mathcal{S},\forall i\geq 0\}. $$ Now we could consider the double orthogonals $^{\bot}(^{\bot}\mathcal{W})$ and $^{\bot}(\mathcal{W}^{\bot})$. It is clear that they are both closed under isomorphisms, extensions, and coproducts.
My question is: are they both localizing Serre subcategories of $R$-Mod in the above sense?
