Symmetric tensor categories in characteristic 2

We construct and study a nested sequence of finite symmetric tensor categories Vec = C-0 subset of C-1 subset of center dot center dot center dot C-n subset of center dot center dot center dot over a field of characteristic 2 such that C-2n are incompressible, i.e., do not admit tensor functors into tensor categories of smaller Frobenius-Perron dimension. This generalizes the category C-1 described by Venkatesh [28] and the category C-2 defined by Ostrik. The Grothendieck rings of the categories C-2n and C2n+1 are both isomorphic to the ring of real cyclotomic integers defined by a primitive 2(n+2)-th root of unity, O-n = Z[2 cos(pi/2(n+1))]. (C) 2019 Elsevier Inc. All rights reserved.