If a: X → A is a cofibration and if R is the adjunction space obtained by attaching A to B by means of b: X → B then {cat}R ≤ min (1 + {cat}A + {cat}B, {cat}X + max ({cat}A, {cat}B)), where cat Y denotes the Lusternik-Schnirelmann category of Y as redefined by G. W. Whitehead, renormalised to take the value 0 on contractible spaces.
