On finiteness properties of polynomial functors

Abstract

We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors from a small symmetric monoidal category whose unit is an initial object to an abelian category (notion introduced in this general setting in the work http://hal.archives-ouvertes.fr/hal-00851869 joint with C. Vespa). We give also an application to functors related to automorphisms of free groups.

52 pages, in French. Version r{é}vis{é}e et largement augment{é}e en juin 2015, modifications mineures en juillet 2015

References in corpus (2)

• FI-modules and stability for representations of symmetric groups
• Noetherian property of infinite EI categories

Cited by in corpus (5)

• Representation stability and finite linear groups
• Homological Invariants of FI-modules and FI_G-modules
• Koszulity of directed categories in representation stability theory
• An application of the theory of FI-algebras to graph configuration spaces
• Asymptotic behaviors of representations of graded categories with inductive functors