Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Groupoids and their Hopf Cyclic Cohomology   A new quantization of groupoids under the name of \times-Hopf coalgebras is
introduced. We develop a Hopf cyclic theory with coefficients in
stable-anti-Yetter-Drinfeld modules for \times-Hopf coalgebras. We use
\times-Hopf coalgebras to study coextensions of coalgebras. Finally,
equivariant \times-Hopf coalgebra Galois coextensions are defined and applied
as functors between categories of stable anti-Yetter-Drinfeld modules over
\times-Hopf coalgebras involved in the coextension.

11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex