LS category: product formulas

Given two continuous maps f :X→Y and g :W→Z between simply connected CW-complexes of finite type, we show that Mcatk(f×g)=Mcatkf+Mcatkg over any field k . Moreover, we establish a characterization Mcatkf=eC∗(Y;k)C∗(X;k) , where e is a kind of Toomer invariant introduced by Félix et al. (1998). Finally, we apply the characterization to show that McatQf=Mcatof .