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?