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arXiv · 2504.20606

Monoidal Relative Categories Model Monoidal $\infty$-Categories

Kensuke Arakawa
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Abstract

We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal $\infty$-categories, and likewise in the symmetric monoidal setting. As an application, we give a concise and complete proof of the fact that every presentably monoidal or presentably symmetric monoidal $\infty$-category is presented by a monoidal or symmetric monoidal model category, which, in the monoidal case, was sketched by Lurie, and in the symmetric monoidal case, was proved by Nikolaus--Sagave.

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Kensuke Arakawa. 2025-04-29. Monoidal Relative Categories Model Monoidal $\infty$-Categories. https://doi.org/10.1016/j.jpaa.2026.108183

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