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Owen Lynch (Feb 19 2022 at 16:55):If we have a symmetric monoidal category, and a lax monoidal functor into , do we get a 2-Operad? Is there a good reference for this?
Owen Lynch (Feb 19 2022 at 17:45):@Sophie Libkind, I feel like I remember talking to you about this over the summer...
Sophie Libkind (Feb 21 2022 at 04:18):Oh that sounds familiar! But unfortunately I don't remember anything beyond what you already said.
Joe Moeller (Feb 22 2022 at 15:15):@Owen Lynch what construction are you trying to generalize here?
Joe Moeller (Feb 22 2022 at 15:16):Given a lax symmetric monoidal functor into , the monoidal Grothendieck construction gives a symmetric monoidal category, and you can take the underlying operad of that. But that's still just a 1-operad. The maps in the fibers get incorporated into the operations.