Strictifying Homotopy Coherent Actions on Hochschild Complexes
Algebraic Topology
2018-12-17 v2 Category Theory
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.
Cite
@article{arxiv.1805.12466,
title = {Strictifying Homotopy Coherent Actions on Hochschild Complexes},
author = {Espen Auseth Nielsen},
journal= {arXiv preprint arXiv:1805.12466},
year = {2018}
}
Comments
Version 2: Corrected typographical errors and added additional details