ScalingStacks

Definition 7.2.2. A morphism of curves $f:Z\to Z^{\prime}$ is a morphism of $1$-dimensional spaces such that

• •

  $f(Z_{u})\subset Z^{\prime}_{u}$

• •

  $f_{|f^{-1}(Z^{\prime}_{o}-Z^{\prime}_{exc})}$ is orientation-preserving

• •

  given $z\in f^{-1}(Z^{\prime}_{exc})$, the canonical map $C(f):C_{Z}(z)\to C_{Z^{\prime}}(f(z))$ is $\iota$-equivariant.