In case anyone finds Puzzles 84 and 85 intimidating, I should add that solving them does not require strokes of brilliant insight: it's a matter of computation.

We know that _if_ the desired right or left adjoint exists, it's given by the formula in [Lecture 6]( So, you can use this formula and see what it gives.

If it gives an undefined answer, the adjoint does not exist. If it's defined, we still aren't sure it's the adjoint. But the [definition of adjoint]( gives a condition one can check using a calculation!

So, it's all a matter of computation... unless one has a clever idea to speed things up.