Polynomial functors from algebras over a set-operad and nonlinear Mackey functors
| Autor: | Christine Vespa, Teimuraz Pirashvili, Manfred Hartl |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 (LAMAV), Centre National de la Recherche Scientifique (CNRS)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Department of Mathematics [Leicester], University of Leicester, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Calculus of functors polynomial functors Derived functor General Mathematics Functor category 010103 numerical & computational mathematics 01 natural sciences Mathematics::Algebraic Topology non-linear Mackey functors Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Adjoint functors Mathematics Discrete mathematics 010102 general mathematics set-operads [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] Natural transformation Ext functor Tor functor Abelian category 18D 18A25 55U |
| Zdroj: | International Mathematics Research Notices. Imrn International Mathematics Research Notices International Mathematics Research Notices, Oxford University Press (OUP), 2015 |
| ISSN: | 1073-7928 1687-0247 |
| Popis: | 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. Comment: 58 pages |
| Databáze: | OpenAIRE |
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