Anindya's clue for Puzzle 278 is worth exploring. Someone please take [the definition of functor](https://forum.azimuthproject.org/discussion/2213/lecture-38-chapter-3-databases/p1), apply it to the functor

\[ \otimes \colon \mathcal{C} \times \mathcal{C} \to \mathcal{C} , \]

and see what each clause actually says.

I'll add that Puzzle 278 is the key to solving Puzzle 280.