On finiteness properties of polynomial functors (Q2804296)

In the present paper the author studies various finiteness properties associated to polynomial functors \(\mathcal{M}_{\mathrm{ini}}\to \mathcal{A}\) from small symmetric monoidal categories such that the unit is an initial object to abelian categories. One of the main results is the following: if \(\mathbf{S}(\mathbb{Z})\) is the category of free abelian groups of finite rank with split monomorphisms then the category of polynomial functors form \(\mathbf{S}(\mathbb{Z})\) to a Grothendieck category is locally noetherian (Theorem 6.25). The paper contains many other interesting results.