# Definition of EnE_{n}-operad in dgCat

In “Derived Algebraic Geometry and Deformation Quantization” Toën defines in 5.1.2 an $$EnE_{n}$$-monoidal A-linear dg-category as an $$EnE_{n}$$-monoid in the symmetric monoidal $$∞\infty$$-category $$dgCatAdgCat_{A}$$ of compactly generated (A-linear) dg-categories.

Concretely, unwrapping this definition Toën says this is equivalent of having a dg-category $$T∈dgCatAT\in dgCat_{A}$$ and morphisms $$En(k)⊗T⊗k→TE_{n}(k)\otimes T^{\otimes k}\to T$$ satisfying the usual conditions of an algebra over an operad.

Question: What are these dg-categories $$En(k)E_{n}(k)$$?

I thought about turning the $$En\mathbb{E}_{n}$$ 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 $$∞−\infty-$$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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Source : Link , Question Author : AT0 , Answer Author : Community