The motivation of the fibrewise unpointed LS category, established by Iwase-Sakai, is the fact that it retrieves the notion of topological complexity of a space in the sense of Farber, which is a numerical homotopy invariant that measures the 'navigational complexity' of X when viewed as the configuration space of a mechanical system. On the other hand the fibrewise pointed LS category, given by James-Morris, retrieves the notion of monoidal topological complexity, a certain variant of topological complexity. 

In this talk we will establish the notion of fibrewise (pointed) sectional category, which is a generalization of the fibrewise (unpointed) LS category and also of the (monoidal) topological complexity. We will give some interesting properties of this new fibrewise homotopy invariant and its pointed version. Also we will analyze in which conditions the unpointed and the pointed versions agree.