ScalingStacks

Lemma 7.1.24. Given $x\in X$, $c\in C(X)$ and $\zeta$ a homotopy class of paths in $X$, we have $m_{f(c)}^{\pm}(f(\zeta))=m_{c}^{\pm}(\zeta)$ and $m_{f(c)}(f(\zeta))=m_{c}(\zeta)$.