  The LS-category of a topological space is a numerical homotopy invariant,
introduced originally in a course on the global calculus of variations by
Lyusternik and Schnirelmann, to estimate the number of critical points of a
smooth function. When the topological space is a smooth manifold equipped with
a proper action of a Lie group, we give a localization formula to calculate the
equivariant analogue of this category in terms of the minimal orbit-type
strata. The formula holds provided that the manifold admits a specific cover.
We show that such a cover exists on every symplectic toric manifold. The known
result stating that the LS-category of a symplectic toric manifold is equal to
the number of fixed points of the torus action follows from our localization
formula.
