Topology Seminar
Speaker: Malthe Sporring (Edinburgh)
Title: Pre-monoidal $\infty$-operads
Date: 15/9/2026
Time: 15:00
Web: http://mat.uab.cat/~topalg
Abstract: Pre-monoidal $\infty$-operads were introduced by Karlsson-Scheimbauer-Walde (under the name pre-coCartesian operads) to describe a class of $\infty$-operads that appears in the study of constructible factorisation algebras. A motivating example is the following: given an object x of a symmetric monoidal category C, one cannot expect the slice category C/x to be symmetric monoidal. However, if the unit is initial, there is always a natural pre-monoidal operad structure on C/x. I will give an overview of this topic and sketch a proof that the natural adjunction between the category of $\infty$-operads and the category of symmetric monoidal $\infty$-categories factors through the category of pre-monoidal $\infty$-operads. This is based on work in progress with Francesca Pratali.