Q: Meaning of pullback functor in a particular setting In Definition B.2.1 of the paper https://arxiv.org/pdf/1211.2851.pdf, the authors state a so-called stability condition:
$$f^{*}(\boldsymbol{\pi}(a, b))=\boldsymbol{\pi}\left(f^{*} a, f^{*} b\right)$$ where $f: \Gamma' \to \Gamma$.
Here, $a: \Gamma \longrightarrow U$,  $b:\left(\Gamma, a^{*}{El}\right) \longrightarrow U$, and  $\boldsymbol{\pi}(a, b): \Gamma \longrightarrow U$.
I can't understand how the pullback functor $f^{\ast}$ is acting on $\boldsymbol{\pi}$, $a$, or $b$. It doesn't seem to me that any of these maps is a morphism in the correct slice category. Any ideas?
