Strictifying Homotopy Coherent Actions on Hochschild Complexes

Espen Auseth Nielsen

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arXiv · 1805.12466

Strictifying Homotopy Coherent Actions on Hochschild Complexes

Espen Auseth Nielsen

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Abstract

If P is a dg-operad acting on a dg-algebra A via algebra homomorphisms, then P acts on the Hochschild complex of A. In the more general case when P is a dg-prop, we show that P still acts on the Hochschild complex, but only up to coherent homotopy. We moreover give a functorial dg-replacement of P that strictifies the action. As an application, we obtain an explicit strictification of the homotopy coherent commutative Hopf algebra structure on the Hochschild complex of a commutative Hopf algebra.

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Espen Auseth Nielsen. 2018-05-31. Strictifying Homotopy Coherent Actions on Hochschild Complexes. https://arxiv.org/abs/1805.12466

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