POLYNOMIAL FUNCTORS FROM ALGEBRAS OVER A SET-OPERAD AND NON-LINEAR MACKEY FUNCTORS
Résumé
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.
Domaines
Topologie algébrique [math.AT]Origine | Fichiers produits par l'(les) auteur(s) |
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