The polyadic convolution conjecture for multiplace multivalued linear maps

Let $\scalebox{1.15}{\textsf{\upshape A}}^{\left(n\right)}$ and $\scalebox{1.15}{\textsf{\upshape C}}^{\left(n'\right)}$ be a polyadic associative algebra and a coassociative coalgebra, respectively, over the same polyadic field $\Bbbk^{\left(m_k,n_k\right)}$. Suppose that both are unital and counital, with polyadic unit and counit maps

$$\bm{\eta}^{\left(r,n\right)}\colon K^{\otimes r}\to A^{\otimes(n-1)},\qquad \bm{\varepsilon}^{\left(n',r'\right)}\colon C^{\otimes(n'-1)}\to K^{\otimes r'}.$$

A polyadic analog of the convolution should be considered for multiplace multivalued $\Bbbk$-linear maps in

$$\operatorname{Hom}_{\Bbbk}\left(C^{\otimes(n'-1)},A^{\otimes(n-1)}\right).$$

This proposal extends the ordinary convolution construction to the case of different algebra and coalgebra arities, $n\ne n'$, and is motivated by the composition $\bm{\eta}^{\left(r,n\right)}\circ\bm{\gamma}^{\left(r',r\right)}\circ\bm{\varepsilon}^{\left(n',r'\right)}$, where the intermediate map is a multiplace multivalued map between tensor powers of the ground object. The source does not state whether this proposal has been established or remains open.