Operads and Computads, Single and Multiple Output

It turns out that there is a problem in creating a well-defined higher categorical structure on the basis of computads (multiple output structures) rather than operads. Before entering this question, it is important to try and understand exactly what “link” or “cellular” restrictions we are subject to, when we restrict ourselves to operads. What types of expressiveness might we gain in the higher categorical context through computads?

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