Homotopy invariance of convolution products

Abstract

The purpose of this paper is to show that various convolution products are fully homotopical, meaning that they preserve weak equivalences in both variables without any cofibrancy hypothesis. We establish this property for diagrams of simplicial sets indexed by the category of finite sets and injections and for tame $M$-simplicial sets, with $M$ the monoid of injective self-maps of the positive natural numbers. We also show that a certain convolution product studied by Nikolaus and the first author is fully homotopical. This implies that every presentably symmetric monoidal $\infty$-category can be represented by a symmetric monoidal model category with a fully homotopical monoidal product.

arXiv commentv2: 31 pages, exposition improved

References in corpus (6)

• Global homotopy theory
• Diagram spaces and symmetric spectra
• On the homotopy groups of symmetric spectra
• Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories
• Diagram spaces, diagram spectra, and spectra of units
• Strictly commutative models for E-infinity quasi-categories

Cited by in corpus (2)

• Global algebraic K-theory
• G-Global Homotopy Theory and Algebraic K-Theory