Warning 15.2.7. In various sources, notably in Lurie (2017), no notational distinction is made between the \(\infty \)-operad \(\OpCocart _C\) and its total \(\infty \)-category \(C^{\amalg }\): both are denoted by \(C^{\amalg }\). Although the notation \(\OpCocart _C\) is slightly more verbose, we find it useful to distinguish between the operad and its total category.
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