POLYNOMIAL FUNCTORS FROM ALGEBRAS OVER A SET-OPERAD AND NON-LINEAR MACKEY FUNCTORS

Manfred Hartl (1) , Teimuraz Pirashvili (2) , Christine Vespa (3)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 Department of Mathematics [Leicester]
3 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: polynomial functors; non-linear Mackey functors; set-operads

Domaines: Topologie algébrique [math.AT]

Manfred Hartl, Teimuraz Pirashvili, Christine Vespa. POLYNOMIAL FUNCTORS FROM ALGEBRAS OVER A SET-OPERAD AND NON-LINEAR MACKEY FUNCTORS. International Mathematics Research Notices, 2015. ⟨hal-00729071v2⟩