The product formula for Lusternik-Schnirelmann category (Q5942493)

The author constructs certain mapping cones \(C\) and \(D\) with the property that for any \(n > 0\), the products of \(C\) and \(D\) with the \(n\)-sphere have category 3 each, and so do those of the squares of \(C\) and \(D\). Thus, he obtains a simply-connected, finite type CW complex \(C\) such that the category of the square of \(C\) is strictly smaller than twice the category of \(C\).