Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Walker's cancellation theorem   Walker's cancellation theorem says that if B+Z is isomorphic to C+Z in the
category of abelian groups, then B is isomorphic to C. We construct an example
in a diagram category of abelian groups where the theorem fails. As a
consequence, the original theorem does not have a constructive proof even if B
and C are subgroups of the free abelian group on two generators. Both of these
results contrast with a group whose endomorphism ring has stable range one,
which allows a constructive proof of cancellation and also a proof in any
diagram category.

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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga