Exercise 4.5.2.12. Show that the diagram of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \emptyset \ar [r] \ar [d] & \{ 0\} \ar [d] \\ \{ 1\} \ar [r] & \Delta ^1 } \]
is a categorical pullback square which is not a homotopy pullback square.