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arXiv · 2603.23018

On the equivalence of two approaches to multiplicative homotopy theories

Kensuke Arakawa
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Abstract

We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their homotopy theories. As consequences, we solve Pavlov's conjecture and obtain a solution to a special case of Hovey's 10th problem. We also prove several variations of the main theorem, such as an analog for non-symmetric monoidal semi-model categories.

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Kensuke Arakawa. 2026-03-24. On the equivalence of two approaches to multiplicative homotopy theories. https://arxiv.org/abs/2603.23018

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