Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The dual of the homotopy category of projective modules satisfies Brown
  representability   We show that the dual of the homotopy category of projective modules over an
arbitrary ring satisfies Brown representability.

8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th