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Tensor product of dendroidal sets

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)


Like any category of presheaves, the category of dendroidal sets is cartesian closed. In this lecture, we will discuss another monoidal structure, which is also closed, and seems more relevant than the cartesian structure. It is closely related to the tensor product of operads introduced by Boardman and Vogt, and it makes the embedding of simplicial sets into dendroidal sets into a strong monoidal functor.


  • Tensor Product
  • Natural Isomorphism
  • Black Vertex
  • Monoidal Structure
  • Symmetric Monoidal Category

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Correspondence to Ieke Moerdijk .

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Moerdijk, I., Toën, B. (2010). Tensor product of dendroidal sets. In: Simplicial Methods for Operads and Algebraic Geometry. Advanced Courses in Mathematics - CRM Barcelona. Springer, Basel.

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