ScalingStacks

Proof. As a right adjoint, $G$ is left exact and therefore preserves $d$-truncated morphisms by T.5.5.6.16. Since $G$ preserves $n$-truncated morphisms and the space of lifts in the square

is homotopy equivalent to the space of lifts in the adjoint square

given by 4.1.4, we see that if $f$ is left orthogonal to all $n$-truncated morphisms then so is $F\left(f\right)$. ∎