Ordnung muss sein
Abstract
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional representations of this partially ordered set. Equivalently, we characterise the length categories that arise as categories of modules over a sheaf of division rings on a finite $T_0$-space.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Rings
Modules
and Algebras
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 February 2026
- Document type
- Preprint