Could an equivalence of categories induce the following isomorphisms?

Question

Let $A,B$ be finite dimensional algebras. If $\mathcal{C}$ is a subcategory of $\mathrm{mod}A$ and there is an equivalence of categories between $\mathcal{C}$ and $\mathrm{mod}B$ ($\mathcal{R}: \mathcal{C} \rightarrow \mathrm{mod} B$ and $\mathcal{S}: \mathrm{mod}B \rightarrow \mathcal{C}$), then for $X \in \mathcal{C}$ and $Y \in \mathrm{mod}B$, are the following isomorphisms right? $$Ext_A^i(\mathcal{S}Y, X) \cong Ext_B^i(Y, \mathcal{R}X),$$ $$Ext_A^i(X,\mathcal{S}Y) \cong Ext_B^i(\mathcal{R}X, Y).$$

Answer 1

No. For example, let $\mathcal{C}$ be the category of semisimple $A$-modules, which is equivalent to $\mathrm{mod }B$ for $B=A/\mathrm{rad }A$. Then $\text{Ext}^i_B$ vanishes for $i>0$, but $\text{Ext}^i_A(X,Y)$ is not necessarily zero for semisimple modules $X$ and $Y$.