REVIEW 2 cited by
Discrete pre-Tannakian categories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these categories generalize finite groups. The main theorem of this paper establishes a rough classification of these categories: we show that any discrete pre-Tannakian $\mathcal{C}$ category is associated to an oligomorphic group $G$, via a construction we recently introduced. In certain cases, such as when $\mathcal{C}$ has enough projectives, we completely describe $\mathcal{C}$ in terms of $G$.
Forward citations
Cited by 2 Pith papers
-
Classification of simple commutative algebras in the Delannoy category
Every simple commutative algebra in the Delannoy category Rep(G), for G = Aut(R,<), is isomorphic to the Schwartz algebra C(R^(n)) of functions on ordered n-tuples; tensor-product relative versions (Theorems B and C) ...
-
Classical interpolation categories
Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.
Discussion (0). Continue with ORCID to comment.