Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classification of tensor categories of two-colored noncrossing
  partitions   Our basic objects are partitions of finite sets of points into disjoint
subsets. We investigate sets of partitions which are closed under taking tensor
products, composition and involution, and which contain certain base
partitions. These so called categories of partitions are exactly the tensor
categories being used in the theory of Banica and Speicher's orthogonal easy
quantum groups. In our approach, we additionally allow a coloring of the
points. This serves as the basis for the introduction of unitary easy quantum
groups, which is done in a separate article. The present article however is
purely combinatorial. We find all categories of two-colored noncrossing
partitions. For doing so, we extract certain parameters with values in the
natural numbers specifying the colorization of the categories on a global as
well as on a local level. It turns out that there are ten series of categories,
each indexed by one or two parameters from the natural numbers, plus two
additional categories. This is just the beginning of the classification of
categories of two-colored partitions and we point out open problems at the end
of the article.

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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph