The Ganea and Whitehead Variants of the\\Lusternik--Schnirelmann Category 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''. Category:55P30