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- W3100693957 abstract "Abstract In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtained by the author in the book [B. Fresse, Homotopy of Operads and Grothendieck–Teichmüller Groups. Part 2. The Applications of (Rational) Homotopy Theory Methods, Math. Surveys Monogr. 217, American Mathematical Society, Providence, 2017]. In short, we prove that the rational homotopy type of such an operad is determined by a cooperad in cochain differential graded algebras (a cochain Hopf dg-cooperad for short) as soon as the Sullivan rational homotopy theory works for the spaces underlying our operad (e.g. when these spaces are connected, nilpotent, and have finite-type rational cohomology groups)." @default.
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- W3100693957 date "2018-10-16" @default.
- W3100693957 modified "2023-09-25" @default.
- W3100693957 title "The extended rational homotopy theory of operads" @default.
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- W3100693957 doi "https://doi.org/10.1515/gmj-2018-0061" @default.
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