Dendroidal set
In mathematics, a dendroidal set is a generalization of simplicial sets introduced by Moerdijk & Weiss (2007). They have the same relation to (colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to categories.
Definition
[edit]A dendroidal set is a contravariant functor from ÎĐ to sets, where ÎĐ is the tree category consisting of finite rooted trees considered as operads, whose morphisms are operad morphisms. The trees are allowed to have some edges with a vertex on only one side; these are called outer edges, and the root is one of the outer edges.
References
[edit]- Moerdijk, Ieke; Weiss, Ittay (2007), "Dendroidal sets", Algebraic & Geometric Topology, 7: 1441â1470, arXiv:math/0701293, doi:10.2140/agt.2007.7.1441, ISSNÂ 1472-2747, MRÂ 2366165
- Dendroidal set at the nLab
