Remark. If in category K(5) the spaces XII and Xi3 are, respectively, fixed spaces A and B, while the spaces X14, Xi5 are points, then the above sequence in the coroUary coincides with the generalized Puppe se- quence obtained by Tsuchida, while if Xll = ~b and X13 , Xi4 , Xi5 are points, we obtain the usual exact Puppe