Commutative Algebra in Tensor Categories
Abstract
Abstract We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some tensor category verifying specific conditions. This is in line with the current program which aims to describe tensor categories by their tensor functors to incompressible categories. We place particular emphasis on the notion of observable subgroups of affine group schemes in tensor categories, which in particular leads to some further insight into observability for classical affine group schemes.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Publication details
- Journal / source
- Transformation Groups
- Publisher
- Springer Science and Business Media LLC
- Volume
- 31
- Issue
- 2
- Pages
- 1225–1272
- Publication date
- 10 April 2026
- Language
- EN