TL;DR
This paper introduces a method to construct super Tannakian hulls for certain rigid tensor categories, providing a universal embedding into super Tannakian categories over characteristic zero fields.
Contribution
It presents a novel construction of super Tannakian hulls for small rigid tensor categories with faithful functors to super vector spaces, extending Tannakian theory.
Findings
Construction of super Tannakian hulls for given tensor categories
Universal property of the hulls analogous to field of fractions
Applicable to categories with faithful tensor functors to super vector spaces
Abstract
We consider essentially small rigid tensor categories (not necessarily abelian) which have a faithful tensor functor to a category of super vector spaces over a field of characteristic 0. It is shown how to construct for each such tensor category a super Tannakian hull, which is a universal faithful tensor functor to a super Tannakian category over a field of characteristic 0. The construction is analogous to the passage from an integral domain to its field of fractions.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology