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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

From $\Gamma$-spaces to algebraic theories


Author: Bernard Badzioch
Journal: Trans. Amer. Math. Soc. 357 (2005), 1779-1799
MSC (2000): Primary 55P48; Secondary 18C10
DOI: https://doi.org/10.1090/S0002-9947-04-03711-0
Published electronically: December 16, 2004
MathSciNet review: 2115076
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Abstract: The paper examines semi-theories, that is, formalisms of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. It is shown that for any semi-theory one can find an algebraic theory describing the same structure on spaces as the original semi-theory. As a consequence one obtains a criterion for establishing when two semi-theories describe equivalent homotopy structures.


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Additional Information

Bernard Badzioch
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Department of Mathematics, University of Buffalo, SUNY, Buffalo, New York 14260-2900
Email: badzioch@math.umn.edu, badzioch@buffalo.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03711-0
Received by editor(s): June 11, 2003
Published electronically: December 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.