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algebraic combinatorics – Generalised operad buildings

We can naively deem an operad as a group $${P(n)}_{ngeq 0}$$ of vector areas $$P(n)$$ consisting of “functions” with $$n$$ inputs and one output, outfitted with plenty of compositions
$$P(m)instances P(n)to P(m+n-1)$$
given by attaching the output of an component of $$P(n)$$ to one of many inputs of an component of $$P(m)$$.

A dioperad generalises this to permit a number of outputs. So we now have a group $${P(n,m)}$$, and a composition
$$P(n_1,m_1)instances P(n_2,m_2)to P(n_1+n_2-1, m_1+m_2-1)$$
the place we connect one output to one enter.

My query is whether or not there’s a related construction within the literature the place we enable ourselves to connect a number of inputs to a number of outputs? Some systematize of poly-operad

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