How does a map of two categorical operads induce a map of categories of generalized multicategories?

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I'm working on a project and I have two categorical operads with a free $\Sigma_n$ action and there exists a map of operads between them. I know via a paper by Elmendorf and others titled "Left Adjoints for Generalized Multicategories" that these categorical operads induce a category of generalized multicategories. I am wondering should it induce a map between these two generaized multicategories?