Abstract
Recall that a dendroidal set X is an ∞-operad if it satisfies the inner Kan condition; i.e., it has the extension property with respect to all inner horn inclusions of trees. In particular, this condition guarantees that if we interpret the sets X(T) as ‘sets of operations’ parametrized by the tree T, then there is a notion of composition of such operations (well-defined up to homotopy) when grafting trees T and Tʹ. In Section 12.1 we introduce an analogous condition for dendroidal spaces, namely the Segal condition. A dendroidal space X satisfying this condition is called a dendroidal Segal space and again there exists a notion of ‘composition of operations’, well-defined up to homotopy.
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Heuts, G., Moerdijk, I. (2022). Dendroidal Spaces and ∞-Operads. In: Simplicial and Dendroidal Homotopy Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-031-10447-3_12
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DOI: https://doi.org/10.1007/978-3-031-10447-3_12
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