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Does the Yoneda lemma translate to the context of operads/multicategories? How about slice operads and fibrations?
Any references or suggestions are welcome, as I'm not quite sure what I'm looking for. I would like to get a better feeling about which intuitions from classical category theory translate into the operadic context.
Hermida has a draft paper entitled Fibrations and Yoneda structure for multicategories answering these questions.