A Tale of Three Homotopies

For a Koszul operad P , there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy 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 f...

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Veröffentlicht in:Applied categorical structures 2016-12, Vol.24 (6), p.845-873
Hauptverfasser: Dotsenko, Vladimir, Poncin, Norbert
Format: Artikel
Sprache:eng
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Zusammenfassung:For a Koszul operad P , there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy 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.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-015-9407-x