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# The Ganea and Whitehead Variants of the\\Lusternik--Schnirelmann Category

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Published:2006-03-01
Printed: Mar 2006
• Jean-Paul Doeraene
• Mohammed El Haouari
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## Abstract

The Lusternik--Schnirelmann category has been described in different ways. Two major ones, the first by Ganea, the second by Whitehead, are presented here with a number of variants. The equivalence of these variants relies on the axioms of Quillen's model category, but also sometimes on an additional axiom, the so-called cube axiom''.
 MSC Classifications: 55P30 - Eckmann-Hilton duality

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