  We present a complete algebraic classification for the curvature tensor in
Weyl-Cartan geometry, by applying methods of eigenvalues and principal null
directions on its irreducible decomposition under the group of global Lorentz
transformations, thus providing a full invariant characterisation of all the
possible algebraic types of the torsion and nonmetricity field strength tensors
in Weyl-Cartan space-times. As an application, we show that in the framework of
Metric-Affine Gravity the field strength tensors of a dynamical torsion field
cannot be doubly aligned with the principal null directions of the Riemannian
Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric
space-times.
