A new invariant of (integrable) homotopy type for foliations is introduced: the tangential category of a foliated manifold.
The classical Lusternik–Schnirelmann theory is generalized to foliations and the relations of the tangential category with other known invariants such as the fibrewise and the equivariant category are studied. Cohomological lower bounds are provided in terms of foliated cohomology.
If the foliation is a product, the tangential category coincides with the ordinary category of the leaves. In general it is just bounded below. Estimates are given of the tangential category for compact-Hausdorff foliations and suspensions. Examples show that the lower and upper bounds are realized.