Noetherian property of infinite EI categories
arXiv:1407.8235
Abstract
It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.
arXiv commentFinal version to appear in NYJM. Remark 3.5 and Example 3.12 Added
References in corpus (6)
- FI-modules and stability for representations of symmetric groups
- FI-modules over Noetherian rings
- GL-equivariant modules over polynomial rings in infinitely many variables
- Representation stability and finite linear groups
- Representation Stability
- FI_W-modules and stability criteria for representations of the classical Weyl groups
Cited by in corpus (16)
- FI-modules and stability for representations of symmetric groups
- Representation stability and finite linear groups
- Categories of FI type: a unified approach to generalizing representation stability and character polynomials
- Homological stability for automorphism groups
- Homological degrees of representations of categories with shift functors
- Koszulity of directed categories in representation stability theory
- Coinduction functor in representation stability theory
- On finiteness properties of polynomial functors
- Representation stability and outer automorphism groups
- An application of Nakayama functor in representation stability theory
- On finite generation in magnitude (co)homology, and its torsion
- Asymptotic behaviors of representations of graded categories with inductive functors
- Castelnuovo-Mumford regularity of representations of certain product categories
- Sheaves of modules on atomic sites and discrete representations of topological groups
- The generalized Auslander-Reiten duality on a module category
- Generators for the representation rings of certain wreath products