Operations on categories of modules are given by Schur functors

Abstract

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes. These operations turn out to be Schur functors associated to $k$-linear representations of symmetric groups. This result is closely related to Macdonald's classification of polynomial functors.

arXiv comment22 pages; complete revision; added references to strict polynomial functors

References in corpus (1)

• Tensor categorical foundations of algebraic geometry

Cited by in corpus (2)

• Using the internal language of toposes in algebraic geometry
• An elementary and constructive proof of Grothendieck's generic freeness lemma