This is in regards to the definition 2.13 of non-deterministic PDA given in Theory of Computation 3rd ed. by Michael Sipser.
The transition is defined as $$ \delta: Q\times \Sigma_\varepsilon \times \Gamma_\varepsilon \to P(Q\times \Gamma_\varepsilon) $$ where $Q$ is the set of states, $\Sigma = \Sigma_\varepsilon\cup \varepsilon$ is input alphabets, and $\Gamma_\varepsilon = \Gamma_\varepsilon\cup \varepsilon$ is the stack alphabets.
I think $\Gamma_\varepsilon$ in the co-domain of the transition should be replaced with $\Gamma_\varepsilon^*$; otherwise, I don't see how this definition can pop/push from/onto its stack.
Please help me clarify this.