Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some approaches towards non-commutative algebraic geometry   The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced
us that commutative rings should be thought of as rings of functions on some
appropriate (commutative) spaces. If we try to push this notion forward we
reach the realm of Non-commutative Geometry. The confluence of ideas comes here
mainly from three seemingly disparate sources, namely, quantum physics,
operator algebras (Connes-style) and algebraic geometry. Following the title of
the article, an effort has been made to provide an overview of the third point
of view. Since na\" ive efforts to generalize commutative algebraic geometry
fail, one goes to the root of the problem and tries to work things out
"categorically". This makes the approach a little bit abstract but not
abstruse. However, an honest confession must be made at the outset - this
write-up is very far from being definitive; hopefully it will provide glimpses
of some interesting developments at least.

3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex