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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mixing categories


Authors: John Oprea and Jeff Strom
Journal: Proc. Amer. Math. Soc. 139 (2011), 3383-3392
MSC (2010): Primary 55M30; Secondary 55P99
Published electronically: March 2, 2011
MathSciNet review: 2811292
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Abstract: We show that $ \mathrm{cat}(X) \leq \mathrm{cat}_1(X) + \mathrm{cat}^1(X)$, where $ \mathrm{cat}_1(X)$ is Fox's $ 1$-dimensional category and $ \mathrm{cat}^1(X)$ is the $ \mathcal{A}$-category of Clapp and Puppe with $ \mathcal{A}=\{$$ \mbox{$1$-dimensional spaces}$$ \}$.


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Additional Information

John Oprea
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
Email: j.oprea@csuohio.edu

Jeff Strom
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008-5200
Email: Jeff.Strom@wmich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10958-4
PII: S 0002-9939(2011)10958-4
Keywords: Lusternik-Schnirelmann category
Received by editor(s): August 22, 2010
Published electronically: March 2, 2011
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.