Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of Hopf Quasigroups   In this paper, we first discuss some properties of the Galois linear maps. We
provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups
as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode
and $G$ be the set of all Hopf quasigroup automorphisms of $H$. We introduce a
new category $\mathscr{C}_{H}(\alpha,\beta)$ with $\alpha,\beta\in G$ over $H$
and construct a new braided $\pi$-category $\mathscr{C}(H)$ with all the
categories $\mathscr{C}_{H}(\alpha,\beta)$ as components.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph