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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 1st 2025
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: \tableofcontents ## Idea A model for [[monoidal (∞,1)-categories]]. ## Definition A __monoidal relative category__ is a [[monoidal category]] equipped with a [[relative category]] structure such that the monoidal product preserves weak equivalences. ## Properties The canonical functor from the quasicategorical localization of the [[relative category]] of monoidal relative categories, monoidal relative functors, and monoidal Dwyer–Kan equivalences to the quasicategory of monoidal quasicategories is a weak equivalence. ## References * Kensuke Arakawa, _Monoidal Relative Categories Model Monoidal ∞-Categories_, [arXiv](https://arxiv.org/abs/2504.20606). <a href="https://ncatlab.org/nlab/revision/monoidal+relative+category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/monoidal+relative+category">current</a>

   Added:

   \tableofcontents

   Idea

   A model for monoidal (∞,1)-categories.

   Definition

   A monoidal relative category is a monoidal category equipped with a relative category structure such that the monoidal product preserves weak equivalences.

   Properties

   The canonical functor from the quasicategorical localization of the relative category of monoidal relative categories, monoidal relative functors, and monoidal Dwyer–Kan equivalences to the quasicategory of monoidal quasicategories is a weak equivalence.

   References

   • Kensuke Arakawa, Monoidal Relative Categories Model Monoidal ∞-Categories, arXiv.

   v1, current