  In this work we study the stability of the four vector irreducible pieces of
the torsion and the nonmetricity tensors in the general quadratic metric-affine
Lagrangian in 4 dimensions. The goal will be to elucidate under which
conditions the spin-1 modes associated to such vectors can propagate in a safe
way, together with the graviton. This highly constrains the theory reducing the
parameter space of the quadratic curvature part from 16 to 5 parameters. We
also study the sub-case of Weyl-Cartan gravity, proving that the stability of
the vector sector is only compatible with an Einstein-Proca theory for the Weyl
vector.
