Polynomial functors from Algebras over a set-operad and non-linear Mackey functors
Abstract
In this paper, we give a description of polynomial functors from (finitely generated free) groups to abelian groups in terms of non-linear Mackey functors generalizing those given in a paper of Baues-Dreckmann-Franjou-Pirashvili published in 2001. This description is a consequence of our two main results: a description of functors from (fi nitely generated free) P-algebras (for P a set-operad) to abelian groups in terms of non-linear Mackey functors and the isomorphism between polynomial functors on (finitely generated free) monoids and those on (finitely generated free) groups. Polynomial functors from (finitely generated free) P-algebras to abelian groups and from (finitely generated free) groups to abelian groups are described explicitely by their cross-e ffects and maps relating them which satisfy a list of relations.
Cite
@article{arxiv.1209.1607,
title = {Polynomial functors from Algebras over a set-operad and non-linear Mackey functors},
author = {Manfred Hartl and Teimuraz Pirashvili and Christine Vespa},
journal= {arXiv preprint arXiv:1209.1607},
year = {2012}
}
Comments
58 pages