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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Stabilizing tensor products

Author: Harold M. Hastings
Journal: Proc. Amer. Math. Soc. 49 (1975), 1-7
MSC: Primary 55E10; Secondary 18D10
MathSciNet review: 0362298
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Abstract: Let $ C$ be a symmetric monoidal category with a suspension, and let SC be the resulting stable category. We shall give necessary and sufficient conditions for extending the symmetric monoidal structure to a monoidal structure on SC. These imply that the usual smash product on finite pointed CW complexes cannot be extended to a smash product (with $ {S^0}$ as unit) on finite spectra, hence not on Boardman spectra. This confirms a conjecture of Alex Heller.

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Keywords: Smash product, stable smash product, Spanier-Whitehead category, stable category, Boardman spectra, monoidal category, symmetric monoidal category, category with suspension
Article copyright: © Copyright 1975 American Mathematical Society

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