Abstract
In this chapter, we develop the Koszul duality theory for operads. We follow the same pattern as for associative algebras: quadratic data, Koszul dual (co)operad, Koszul complex and Koszul resolution. This last one provides us with the minimal model of the operad 
, thereby defining the notion of 
-algebra up to homotopy. In the last section, we extend this method to inhomogeneous quadratic operads.
Les maths, c’est comme l’amour, ça ne s’apprend pas dans les livres mais en pratiquant.
Adrien Douady (private communication)
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Loday, JL., Vallette, B. (2012). Koszul Duality of Operads. In: Algebraic Operads. Grundlehren der mathematischen Wissenschaften, vol 346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30362-3_7
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DOI: https://doi.org/10.1007/978-3-642-30362-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30361-6
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