In “Derived Algebraic Geometry and Deformation Quantization” Toën defines in 5.1.2 an En-monoidal A-linear dg-category as an En-monoid in the symmetric monoidal ∞-category dgCatA of compactly generated (A-linear) dg-categories.

Concretely, unwrapping this definition Toën says this is equivalent of having a dg-category T∈dgCatA and morphisms En(k)⊗T⊗k→T satisfying the usual conditions of an algebra over an operad.

Question: What are these dg-categories En(k)?I thought about turning the En operad defined by Lurie in Higher Algebra into a dg-category, but Im unsure if this would be correct or if it would be relatively easier than giving a direct definition.

I’m not very experienced in operads in general and ∞−operads in particular, so I apologize if the question has an immediate answer or if it comes from a fundamental misunderstanding of the topic.

**Answer**

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