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Answers

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Model structure on the category of small $A_\infty$ categories, hocolims.

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Model category structures on the category of $L_\infty$-algebras

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Reference for functors in Kadeishvili’s C_\infty paper

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Semidirect products and PROPs

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Definition of an E-infinity algebra

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Poincare duality and the $A_\infty$ structure on cohomology (2)

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Higher homotopy algebraic structure on the homology of an operad