Open Collections

Description

In this talk I will explain how the use of functors defined on the category \(I\) of finite sets and injections makes it possible to replace \(E\)-infinity objects by strictly commutative ones. For example, an \(E\)-infinity space can be replaced by a strictly commutative monoid in \(I\)-diagrams of spaces. The quasi-categorical version of this result is one building block for an interesting rigidification result about multiplicative homotopy theories: we show that every presentably symmetric monoidal infinity-category is represented by a symmetric monoidal model category. This is a report on joint work with Christian Schlichtkrull, with Dimitar Kodjabachev, and with Thomas Nikolaus.