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A Tale of Three Homotopies

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Abstract

For a Koszul operad \(\mathcal {P}\), there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy \(\mathcal {P}\)-algebras. Some of those approaches are known to give rise to the same notions. We exhibit the missing links between those notions, thus putting them all into the same framework. The main nontrivial ingredient in establishing this relationship is the homotopy transfer theorem for homotopy cooperads due to Drummond-Cole and Vallette.

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Authors and Affiliations

  1. School of Mathematics, Trinity College, Dublin 2, Dublin, Ireland

    Vladimir Dotsenko

  2. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, 6, Rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Grand Duchy of Luxembourg

    Norbert Poncin

Authors
  1. Vladimir Dotsenko
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  2. Norbert Poncin
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Corresponding author

Correspondence to Vladimir Dotsenko.

Additional information

The research of the authors was supported by Grant GeoAlgPhys 2011–2013 awarded by the University of Luxembourg.

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Dotsenko, V., Poncin, N. A Tale of Three Homotopies. Appl Categor Struct 24, 845–873 (2016). https://doi.org/10.1007/s10485-015-9407-x

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  • DOI: https://doi.org/10.1007/s10485-015-9407-x

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