Monoidal relative categories model monoidal ∞-categories
Abstract
We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal ∞-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 ∞-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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Logic
programming
and type systems
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 2
- Pages
- 108183–108183
- Publication date
- 27 January 2026
- Language
- EN