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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeNov 3rd 2017
   • (edited Nov 3rd 2017)
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexI heard from a few people (including a student of Moerdijk) and looked into it, and the [closed monoidal structure](https://ncatlab.org/nlab/show/dendroidal+set#ClosedMonoidalStructure) on dendroidal sets has been shown to not exist. There is a tensor product functor, but it fails to be associative and closed, and explicit counterexamples have now been found. I don't have enough expertise with dendroidal sets to fix the article, but what the nLab says right now is incorrect. There have been multiple errata published on some of the earlier papers. Luckily, none of the important proofs have depended in an essential way on this property of the tensor product, but a few have had to be rewritten to take this into account. The latest papers on Dendroidal sets now use a lax monoidal structure rather than a true monoidal structure, see: [this MO question](https://mathoverflow.net/questions/198051/tensor-product-of-dendroidal-sets-counter-examples) and [HHM 15](https://arxiv.org/pdf/1305.3658v3.pdf)

   I heard from a few people (including a student of Moerdijk) and looked into it, and the closed monoidal structure on dendroidal sets has been shown to not exist. There is a tensor product functor, but it fails to be associative and closed, and explicit counterexamples have now been found. I don’t have enough expertise with dendroidal sets to fix the article, but what the nLab says right now is incorrect. There have been multiple errata published on some of the earlier papers. Luckily, none of the important proofs have depended in an essential way on this property of the tensor product, but a few have had to be rewritten to take this into account.

   The latest papers on Dendroidal sets now use a lax monoidal structure rather than a true monoidal structure, see:

   this MO question

   and

   HHM 15

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 3rd 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have known this for a long time, but I didn't remember that the false statement is still kept on the nLab. So thanks for the alert, I have removed it now. Somebody should fill in more details [here](https://ncatlab.org/nlab/show/dendroidal+set#ClosedMonoidalStructure). I won't be touchig that entry anymore.

   I have known this for a long time, but I didn’t remember that the false statement is still kept on the nLab. So thanks for the alert, I have removed it now.

   Somebody should fill in more details here. I won’t be touchig that entry anymore.