I saw the definition of bimodule and the tensor-hom adjunction on it: the Tensor-Hom adjunction , and the tensor-hom adjunction of $\mathscr{O}_X$-modules: Stacks01CN
Can the case of $\mathscr{O}_X$-modules be considered as some kind of $(\mathscr{O}_X, \mathscr{O}_Y)$-modules and extended the tensor-hom adjunction to
$$ \mathcal{H o m}_{\mathcal{O}_X}\left(\mathcal{F} \otimes_{\mathcal{O}_Y} \mathcal{G}, \mathcal{H}\right) \longrightarrow \mathcal{Hom}_{{\mathcal{O}_Y}}\left(\mathcal{F}, \mathcal{H o m}_{\mathcal{O}_X}(\mathcal{G}, \mathcal{H})\right) $$
? What should be the definition for bimodule on ringed spaces? Derived hom-tensor adjunction for $O_X$-modules seems related. Nevertheless it’s stated in more advanced language then I can understand.
Thank you very much