Fibered category: The object is not in the pullback, what is it mapped to? Given two objects and their intersection which is the pullback, what is the pullback of any sub-object that is not in the intersection?
For instance given the category:
$
\begin{matrix}
    4 &amp; \xrightarrow{p_{2}} &amp; \{4,5,6,7 \}
    \\
     p_{1} \; \downarrow &amp;&amp; \beta \downarrow
    \\
     \{1,2,3,4\} &amp; \xrightarrow{\alpha} &amp; c =\{1,2,3,4,5,6,7\} 
\end{matrix}
$
The concept you need to consider is &quot;diagram commutes&quot;. The pullback diagram creates a subset of $\alpha \times \beta$ which contains only the elements of $(a,b)$ which makes the diagram commute.
The concept you need to consider is &quot;diagram commutes&quot;. The pullback diagram creates a subset of $\alpha \times \beta$ which contains only the elements of $(a,b)$ which makes the diagram commute.