POLYNOMIAL FUNCTORS FROM ALGEBRAS OVER A SET-OPERAD AND NON-LINEAR MACKEY FUNCTORS - Archive ouverte HAL
Article Dans Une Revue International Mathematics Research Notices Année : 2015

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.
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Dates et versions

hal-00729071 , version 1 (07-09-2012)
hal-00729071 , version 2 (10-09-2012)

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Citer

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⟩
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