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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 11th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Idea The analogue of the [[Joyal model structure]] for [[cubical sets]], with or without connection. ## Related concepts * [[Joyal model structure]], [[quasicategory]] * [[cubical set]], [[cubical set with connection]] ## References With connections (positive, negative, or both): * [[Brandon Doherty]], [[Chris Kapulkin]], [[Zachery Lindsey]], [[Christian Sattler]], _Cubical models of (∞,1)-categories_, [arXiv:2005.04853](https://arxiv.org/abs/2005.04853) Without connections: * [[Brandon Doherty]], _Cubical models of higher categories without connections_, [arXiv:2207.03636](https://arxiv.org/abs/2207.03636). <a href="https://ncatlab.org/nlab/revision/model+structure+for+cubical+quasicategories/1">v1</a>, <a href="https://ncatlab.org/nlab/show/model+structure+for+cubical+quasicategories">current</a>

   Created:

   Idea

   The analogue of the Joyal model structure for cubical sets, with or without connection.

   Related concepts

   • Joyal model structure, quasicategory

   • cubical set, cubical set with connection

   References

   With connections (positive, negative, or both):

   • Brandon Doherty, Chris Kapulkin, Zachery Lindsey, Christian Sattler, Cubical models of (∞,1)-categories, arXiv:2005.04853

   Without connections:

   • Brandon Doherty, Cubical models of higher categories without connections, arXiv:2207.03636.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 12th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexInteresting, had not seen this before. Have added to the first reference: > Memoirs of the AMS ([accepted 2022](https://www.ams.org/cgi-bin/mstrack/accepted_papers/memo)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+for+cubical+quasicategories/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+for+cubical+quasicategories/2">v2</a>, <a href="https://ncatlab.org/nlab/show/model+structure+for+cubical+quasicategories">current</a>

   Interesting, had not seen this before. Have added to the first reference:

   Memoirs of the AMS (accepted 2022)

   diff, v2, current