Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian categories in dimension 2   The goal of this thesis is to define a 2-dimensional version of abelian
categories, where symmetric 2-groups play the role that abelian groups played
in 1-dimensional algebra. Abelian and 2-abelian groupoid enriched categories
are defined and it is proved that homology can be developed in them, including
the existence of a long exact sequence of homology corresponding to an
extension of chain complexes. This generalises known results for symmetric
2-groups. The examples include, in addition to symmetric 2-groups, the
2-modules on a 2-ring, which form a 2-abelian groupoid enriched category.
Moreover, internal groupoids, functors and natural transformations in an
abelian category C (in particular, Baez-Crans 2-vector spaces) form a 2-abelian
groupoid enriched category if and only if the axiom of choice holds in C.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess