A prop structure on partitions

25.04.2025, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Coline Emprin (ENS, Paris) (online)

PROPs were introduced by Mac Lane in 1965 as a special type of category whose objects are natural numbers, endowed with an additional horizontal composition of morphisms beyond the usual categorical composition. In this talk, I will present a specific PROP structure that emerges from the combinatorics of partitions. The construction of this structure is closely related to the Karoubi envelope of a certain category, which I will introduce along the way. This PROP is of particular interest in the context of functor homology, as its composition corresponds to the Yoneda product of extension groups between exterior power functors. I will conclude by discussing how such constructions can be used to compute extension groups between simple functors defined on free groups.
This is joint work with Dana Hunter, Muriel Livernet, Christine Vespa, and Inna Zakharevich.