= Tetrad postulate
{title2=$\partial_a e^\mu{}_b+\omega_a{}^\mu{}_{\nu}e^\nu{}_b-\Gamma^c{}_{ab}e^\mu{}_c=0$}
The <tetrad postulate> expresses compatibility of the spacetime and Lorentz-frame connections on a <vierbein>. For the inverse coframe $e_\nu{}^b$, solving gives $\omega_a{}^\mu{}_{\nu}=e_\nu{}^b(\Gamma^c{}_{ab}e^\mu{}_c-\partial_a e^\mu{}_b)$. <Metric compatibility> makes the lowered connection antisymmetric in its Lorentz indices. Lifting this connection through the <Spinor representation of the Lorentz group> defines the <spinor covariant derivative>.
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