Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two characterizations of finite quasi-Hopf algebras   Let H be a finite-dimensional quasibialgebra. We show that H is a quasi-Hopf
algebra if and only if the category of its finite-dimensional left modules is
rigid if and only if a structure theorem for Hopf modules over H holds. We also
show that a dual structure theorem for Hopf modules over a coquasibialgebra H
holds if and only if the category of finite-dimensional right H-comodules is
rigid; this is not equivalent to H being a coquasi-Hopf algebra.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat