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Sep 26, 2014 at 10:19 comment added Dmitri Pavlov @GabrielC.Drummond-Cole: Of course! The category of operads itself is the category of algebras over a certain colored operad (the “operad of operads”), so this example is covered by the main post. The example that I have in mind is that of enriched categories in enriched categories, i.e., higher enriched categories.
Sep 25, 2014 at 18:13 comment added Gabriel C. Drummond-Cole The same motivation applies to calculating homotopy pushouts of operads themselves.
Sep 25, 2014 at 16:28 history asked Dmitri Pavlov CC BY-SA 3.0