ScalingStacks

Proposition 2.86. Let $\phi:A_{Z}\to A_{W}$ be a homomorphism of $k$-algebras of finite type where $Z=\spec(A_{Z})$ and $W=\spec(A_{W})$. Then there is an induced continuous map $\phi^{\star}:W^{an}\to Z^{an}$, which sends a multiplicative seminorm $|\cdot|_{w}$ to $|\phi(\cdot)|_{w}$.