Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-abelian higher gauge theory and categorical bundle   A gauge theory is associated with a principal bundle endowed with a
connection permitting to define horizontal lifts of paths. The horizontal lifts
of surfaces cannot be defined into a principal bundle structure. An higher
gauge theory is an attempt to generalize the bundle structure in order to
describe horizontal lifts of surfaces. A such attempt is particularly difficult
for the non-abelian case. Some structures have been proposed to realize this
goal (twisted bundle, gerbes with connection, bundle gerbe, 2-bundle). Each of
them uses a category in place of the total space manifold of the usual
principal bundle structure. Some of them replace also the structure group by a
category (more precisely a Lie crossed module viewed as a category). But the
base space remains still a simple manifold (possibly viewed as a trivial
category with only identity arrows). We propose a new principal categorical
bundle structure, with a Lie crossed module as structure groupoid, but with a
base space belonging to a bigger class of categories (which includes
non-trivial categories), that we call affine 2-spaces. We study the geometric
structure of the categorical bundles built on these categories (which is a more
complicated structure than the 2-bundles) and the connective structures on
these bundles. Finally we treat an example interesting for quantum dynamics
which is associated with the Bloch wave operator theory.

31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph