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Polynomial Functors from Algebras Over a Set-Operad and Nonlinear Mackey Functors

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journal contribution
posted on 22.10.2019, 11:19 by Manfred Hartl, Teimuraz Pirashvili, Christine Vespa
In this paper, we give a description of polynomial functors from (finitely generated free) groups to abelian groups in terms of nonlinear 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 (finitely generated free) P-algebras (for P a set-operad) to abelian groups in terms of nonlinear 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 explicitly by their cross-effects and maps relating them which satisfy a list of relations.

Funding

The authors gratefully acknowledge the hospitality of the Max Planck Institut für Mathematik in Bonn where this project started and where this paper was written.

History

Citation

International Mathematics Research Notices, 2015 (6), pp. 1461-1554 (94)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

International Mathematics Research Notices

Publisher

Oxford University Press (OUP)

issn

1073-7928

eissn

1687-0247

Acceptance date

23/10/2013

Copyright date

2013

Available date

22/10/2019

Publisher version

https://academic.oup.com/imrn/article/2015/6/1461/668187

Language

en