Dendroidal set
In mathematics, a dendroidal set is a generalization of simplicial sets introduced by {{harvtxt|Moerdijk|Weiss|2007}}.
They have the same relation to (colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to categories.
Definition
A dendroidal set is a contravariant functor from Ω to sets, where Ω 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
- {{Citation | last1=Moerdijk | first1=Ieke | last2=Weiss |author1link = Ieke Moerdijk| first2=Ittay | title=Dendroidal sets | doi=10.2140/agt.2007.7.1441 | mr=2366165 | year=2007 | journal=Algebraic & Geometric Topology | issn=1472-2747 | volume=7 | pages=1441–1470| arxiv=math/0701293 }}
- {{nlab|id=dendroidal+set|title=Dendroidal set}}