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Given a pair of Koszul dual algebras, say `$S^*(V)$` and `$\bigwedge^*(V^*)$` for some vector space $V$, one obtains an a triangulated equivalence between their bounded derived categories of finitely-generated graded modules.

Given a pair of Koszul dual operads, say the Lie and commutative operads, what is the precise analogue of a derived equivalence between their categories of algebras?

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# koszul duality and algebras over operads

Given a pair of Koszul dual algebras, say `$S^*(V)$` and `$\bigwedge^*(V^*)$` for some vector space $V$, one obtains an equivalence between their bounded derived categories of finitely-generated graded modules.

Given a pair of Koszul dual operads, say the Lie and commutative operads, what is the precise analogue of a derived equivalence between their categories of algebras?
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