Lusternik-Schnirelmann cocategory (Q1320923)

A new definition of cocategory is introduced that dualizes Whitehead's definition of category. It is then proved that if \(\text{cocat} X \leq n\), all Whitehead products of length \(>n\) vanish. On the other hand, for a rational space \(X\), \(\text{cocat} X \leq \text{cocat}_ 0X\) where \(\text{cocat}_ 0X\) is the rational homotopy invariant introduced by Sbai in terms of Quillen minimal models to approximate \(\text{cocat} X\).