Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quotients of \'etale groupoids and the abelianizations of groupoid
  C*-algebras   In this paper, we introduce quotients of \'etale groupoids. Using the notion
of quotients, we describe the abelianizations of groupoid C*-algebras. As
another application, we obtain a simple proof that effectiveness of an \'etale
groupoid is implied by the full uniqueness property of its groupoid C*-algebra.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin