On the equivalence of two approaches to multiplicative homotopy theories

Abstract: Locally presentable (\infinity,1) categories admit two popular models: Presentable quasicategories and combinatorial model categories. Building on the foundational work of Dugger and Lurie, Pavlov proved that their associated (\infty,1)-categories are equivalent, confirming a long-standing expectation. He then went on to conjecture that this should also hold multiplicatively, i.e., for presentably symmetric monoidal quasicategories and combinatorial symmetric monoidal model categories. Such an equivalence would be of foundational importance in higher algebra.

In arXiv:2603.23018, I proved this conjecture. The main difficulty is that existing techniques to rigidify quasicategories often break down multiplicatively. In the talk, I will explain how to overcome this. If time permits, I will also explain applications to enriched infinity operads (arXiv:2603.23019).

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

( paper )

Topology and Geometry Seminar (Texas, Kansas)