# Do equivariant morphisms induce representable maps of quotient stacks?

Let $f: X \to Y$ be a $G$-equivariant map between schemes $X$, $Y$ with action of a flat group scheme $G$. Then why is the induced map of algebraic stacks $[X/G] \to [Y/G]$ representable?

first, $Y\to [Y/G]$ is a chart
$$\require{AMScd} \begin{CD} X @>>> Y \\ @VVV @VVV \\ [X/G] @>>> [Y/G] \end{CD}$$ is cartesian (this is so because any morphism between two $G$-torsors is an isomorphism).