ScalingStacks

Proposition 7.4.13. Let $f:Z\to Z^{\prime}$ be a morphism of curves and let $\theta^{\prime}$ be a non-zero map in ${\mathcal{P}}^{\bullet}(Z^{\prime})$. Then $f^{\#}(\theta^{\prime})$ is a sum of maps $\theta$ such that $f(\deg_{Z_{f}^{+}}(\theta))=\deg_{f(Z_{f})^{+}}(\theta^{\prime})$.