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COMMENT
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The categorical sequence for a CW complex X is the sequence whose n-th term is the smallest m for which the Lusternik-Schnirelmann category of the m-skeleton is equal to n (or else infinity if there is no such m).
All categorical sequences begin with a_0 = 0. It can be shown that for all categorical sequences, a_{k+l} >= a_k + a_l.
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REFERENCES
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Cornea, Octav; Lupton, Gregory; Oprea, John; Tanre, Daniel. Lusternik-Schnirelmann category. Mathematical Surveys and Monographs, 103. American Mathematical Society, Providence, RI, 2003.
R. Nendorf, N. Scoville, J. Strom, Categorical Sequences, preprint, 2004.
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