Download PDFOpen PDF in browserWalker's Cancellation Theorem3 pages•Published: July 28, 2014AbstractWalker's cancellation theorem says that if B + Z isisomorphic 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. In fact, in our example B and C are subgroups of Z<sup>2</sup>. 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. Keyphrases: abelian groups, constructivism, diagram category, kripke model In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 145-147.
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