= Halo-to-galaxy luminosity mapping
{title2=$\Phi(L)=n_h(M_h)\left|dM_h/dL\right|$}
A monotonic luminosity assignment to a counted halo population converts its differential abundance per mass into a <luminosity function> by a change of variable. If $n_h\propto M_h^{-a}$ and $L\propto M_h^p$, then $\Phi\propto L^{-1-(a-1)/p}$. This simple mapping assumes one counted galaxy per halo, no scatter and a fixed selection. A mass-dependent <baryon conversion efficiency of a halo>, satellites and stellar-population differences modify it.
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