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In our recent paper Shoikhet [ 47 ], a version of the “generalized Deligne conjecture” for abelian   $n$  -fold monoidal categories is proven. For   $n=1,$   this result says that, given an abelian monoidal   $\Bbbk$  -linear category   $\mathcal{A}$   with unit   $e$  ,   ${\operatorname{char}}\Bbbk=0$  ,   ${\mathrm{RHom}}_{\mathcal{A}}(e,e)$   is the first component of a Leinster 1-monoid in   ${{\mathcal{A}lg}}(\Bbbk)$   (provided a rather mild condition on the monoidal and the abelian structures in   $\mathcal{A}$  , called homotopy compatibility, is fulfilled).

Graded Leinster Monoids and Generalized Deligne Conjecture for 1-Monoidal Abelian Categories