Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A survey on the Koszul homology algebra   The Koszul homology algebra of a commutative local (or graded) ring $R$ tends
to reflect important information about the ring $R$ and its properties. In
fact, certain classes of rings are characterized by the algebra structure on
their Koszul homologies. In this paper we survey some classical results on the
Koszul homology algebras of such rings and highlight some applications. We
report on recent progress on the Koszul homology algebras of Koszul algebras
and examine some open questions on the topic.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
16
The categories of this paper are: stat