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Hey everyone,
I feel like this must be written down somewhere, and you all are probably the most knowledgeable about such things. Given a monoidal category, if I take its underlying multicategory, take the free symmetric multicategory thereon, followed by the category of operators, does this thing admit a Grothendieck opfibration to the category of operators of the free symmetric multicategory associated to the associative operad (i.e. the category of operators of the multicategory with one object and mapping sets given by the symmetric groups)? This seems certainly true, but I’m more interested in finding a place where this is written down so I can cite it directly (trying to avoid going into too significant detail on multicategories in a paper I’m writing).
Thanks for any kind of references to check out!
-Jon
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