Dendroidal Spaces and ∞-Operads

Abstract Recall that a dendroidal set X is an ∞-operad if it satisfies the inner Kan condition; i.e., has extension property with respect to all horn inclusions of trees. In particular, this condition guarantees we interpret sets X(T) as ‘sets operations’ parametrized by tree T, then there notion composition such operations (well-defined up homotopy) when grafting trees T and Tʹ. Section 12.1 introduce analogous for spaces, namely Segal condition. A space satisfying called again exists ‘composition operations’, well-defined homotopy.