  In this short pedagogical note we clarify some subtleties concerning the
symmetries of the coefficients of a Riemann-Cartan connection and the
symmetries of the coefficients of the contorsion tensor that has been a source
of some confusion in the literature, in particular in a so called 'ECE theory'.
We show in details that the coefficients of the contorsion tensor of a
Riemann-Cartan connection has a symmetric part and an antisymmetric part, the
symmetric part defining the strain tensor of the connection. Moreover, the
contorsion tensor has also a bastard anti-symmetry when written with all its
indices in the `covariant' positions.
