The Lusternik–Schnirelmann category of certain infinite CW-complexes

Examples are constructed to illustrate: (i) The LS category of a 1-connected, finite type CW-complex X which is the homotopy colimit of a sequence X1→X2→X3→⋯ of 1-connected, finite CW-complexes may exceed the LS category of each Xi; and (ii) LS category is not an invariant of the localization genus of a 1-connected, finite type CW-complex.