From Γ-spaces to algebraic theories

Badzioch, Bernard

doi:10.1090/S0002-9947-04-03711-0

From $\Gamma$-spaces to algebraic theories
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by Bernard Badzioch

Trans. Amer. Math. Soc. 357 (2005), 1779-1799

DOI: https://doi.org/10.1090/S0002-9947-04-03711-0

Published electronically: December 16, 2004

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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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