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The bar construction of an algebra as an E-infinite Hopf algebra

Benoit Fresse
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Abstract

We prove that the bar construction of an $E_\infty$ algebra forms an $E_\infty$ algebra. To be more precise, we provide the bar construction of an algebra over the surjection operad with the structure of a Hopf algebra over the Barratt-Eccles operad. (The surjection operad and the Barratt-Eccles operad are classical $E_\infty$ operads.)

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Benoit Fresse. 2003-07-25. The bar construction of an algebra as an E-infinite Hopf algebra. https://arxiv.org/abs/math/0303027

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