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Register a new userLocally constant n-operads as higher braided operads
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Authors
M. A. Batanin
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We introduce a category of locally constant $n$-operads which can be considered as the category of higher braided operads. For $n=1,2,infty$ the homotopy category of locally constant $n$-operads is equivalent to the homotopy category of classical nonsymmetric, braided and symmetric operads correspondingly.
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We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial presheaves for a certain category of undirected graphs. This new category of undirected graphs, denoted $mathbf{U}$, plays a similar role for modular operads that the dendroidal category $Omega$ plays for operads. We carefully study properties of $mathbf{U}$, including the existence of certain factorization systems. Related structures, such as cyclic operads and stable modular operads, can be similarly treated using categories derived from $mathbf{U}$.
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