Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic structures on valuations, their properties and applications   We describe various structures of algebraic nature on the space of continuous
valuations on convex sets, their properties (like versions of Poincar\'e
duality and hard Lefschetz theorem), and their relations and applications to
integral geometry.

35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph