Consider the operation \\(C_f \\) defined to be the pullback followed by the pushout.

$$
C_f := f_* \circ f^*.
$$

**Puzzle KP2.** Extending [this puzzle](https://forum.azimuthproject.org/discussion/comment/16320/#Comment_16320) in lecture 4, treat \\(C_f\\) as a monad, and find it's 'unit' and 'multiplication' natural transformations.