Re. Puzzles (16) by John Baez: I'm having trouble seeing how there can be a natural transformation that's not an isomorphism for Sophie's example. Since \\(C\\) has just 1 object, a transformation \\(F \rightarrow G\\) consists of just one map \\(F(\textrm{Person}) \rightarrow G(\textrm{Person}) \\). There are only \\(2^2 = 4\\) possibilities for this map; 2 of which are bijections giving rise to natural isomorphisms, and the other 2 cannot satisfy the naturality condition. Am I missing something?