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Des propriétés de finitude des foncteurs polynomiaux

Volume 233 / 2016

Aurélien Djament Fundamenta Mathematicae 233 (2016), 197-256 MSC: 18A25, 18D10, 18E15, 18E35. DOI: 10.4064/fm954-8-2015 Published online: 22 January 2016


We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups $\mathbb {Z}^n$ with split monomorphisms to abelian groups is “almost” locally noetherian. We also give an application to functors related to automorphisms of free groups.


  • Aurélien DjamentCNRS, laboratoire de mathématiques Jean Leray (UMR 6629)
    2 rue de la Houssinière, BP 92208
    44322 Nantes Cedex 3, France

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