  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.
