Deligne conjecture for higher-monoidal abelian categories

We discuss and outline a proof of some generalization of “Deligne conjecture” for $n$-fold monoidal abelian categories. We illustrate it in two examples: the category of bimodules over an associative algebra ($n=1$), and the category of tetramodules over a Hopf algebra ($n=2$). As well, we discuss some approach to formality phenomena in deformation theory, natural from this point of view.