Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groupoids and $C^*$-algebras for left cancellative small categories   Categories of paths are a generalization of several kinds of oriented
discrete data that have been used to construct $C^*$-algebras. The techniques
introduced to study these constructions apply almost verbatim to the more
general situation of left cancellative small categories. We develop this theory
and derive the structure of the $C^*$-algebras in the most general situation.
We analyze the regular representation, and the Wiener-Hopf algebra in the case
of a subcategory of a groupoid.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con