  We generalize results from topological robotics on the topological complexity
(TC) of aspherical spaces to sectional categories of fibrations inducing
subgroup inclusions on the level of fundamental groups. In doing so, we
establish new lower bounds on sequential TCs of aspherical spaces as well as
the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber
canonical class for TC to classes for sequential TCs and explore their
properties. We combine them with the results on sequential TCs of aspherical
spaces to obtain results on spaces that are not necessarily aspherical.
