John – thank you for the clarifications from [comment #9](https://forum.azimuthproject.org/discussion/comment/19670/#Comment_19670); they were all very valuable.

My misunderstanding stemmed from the fact that I thought it's enough to show that there exists a bijection between the two hom-sets.

This misunderstanding was reinforced by [my solution](https://forum.azimuthproject.org/discussion/comment/19577/#Comment_19577) to puzzle 150, which I now realize is incomplete since I didn't state explicitly what is the natural isomorphism between the two hom-sets.

When I solved that puzzle I was thinking more in terms of cardinality of sets (if two sets have the same cardinality there is a bijection between them), but I was not concerned with choosing a particular bijection.

My misunderstanding stemmed from the fact that I thought it's enough to show that there exists a bijection between the two hom-sets.

This misunderstanding was reinforced by [my solution](https://forum.azimuthproject.org/discussion/comment/19577/#Comment_19577) to puzzle 150, which I now realize is incomplete since I didn't state explicitly what is the natural isomorphism between the two hom-sets.

When I solved that puzzle I was thinking more in terms of cardinality of sets (if two sets have the same cardinality there is a bijection between them), but I was not concerned with choosing a particular bijection.