A prop structure on partitions
Algebraic Topology
2024-02-21 v1
Abstract
Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Yoneda product of extensions between exterior power functors.
Keywords
Cite
@article{arxiv.2402.12895,
title = {A prop structure on partitions},
author = {Coline Emprin and Dana Hunter and Muriel Livernet and Christine Vespa and Inna Zakharevich},
journal= {arXiv preprint arXiv:2402.12895},
year = {2024}
}