The Grothendieck Construction for -Categories Fibered over Categorical Patterns

We show how to treat families of -categories fibered in categorical patterns (e. g. , -operads and monoidal -categories) in terms of fibrations by relativizing the Grothendieck construction. As applications, we construct an analog of the universal cocartesian fibration and explain how to compute limits and colimits of -categories fibered in categorical patterns.