Abstract
Given two continuous maps f :X→Y and g :W→Z between simply connected CW-complexes of finite type, we show that Mcat k (f×g)=Mcat k f+Mcat k g over any field k . Moreover, we establish a characterization Mcat k f=e C ∗(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 Mcat Q f=Mcat of .
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