  Vorst and latter Dayton-Weibel proved that K_n-regularity implies
K_(n-1)-regularity. In this note we generalize this result from (commutative)
rings to differential graded categories and from algebraic K-theory to any
functor which is Morita invariant, continuous, and localizing. Moreover, we
show that regularity is preserved under taking desuspensions, fibers of
morphisms, direct factors, and arbitrary direct sums. As an application, we
prove that the above implication also holds for schemes. Along the way, we
extend Bass' fundamental theorem to this broader setting and prove a Nisnevich
descent result which is of independent interest
