Let \\(\mathcal{C}\\) be an arbitrary category and let \\(\mathcal{P}\\) be a preorder, thought of as a category.

Consider the following statements:

1. For any two functors \\(F, G : \mathcal{C} \rightarrow \mathcal{P}\\), there is at most one natural transformation

\\(F \rightarrow G\\).

2. For any two functors \\(F, G : \mathcal{P} \rightarrow \mathcal{C}\\), there is at most one natural transformation

\\(F \rightarrow G\\).

For each, if it is true, say why; if it is false, give a counterexample.

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Consider the following statements:

1. For any two functors \\(F, G : \mathcal{C} \rightarrow \mathcal{P}\\), there is at most one natural transformation

\\(F \rightarrow G\\).

2. For any two functors \\(F, G : \mathcal{P} \rightarrow \mathcal{C}\\), there is at most one natural transformation

\\(F \rightarrow G\\).

For each, if it is true, say why; if it is false, give a counterexample.

[Previous](https://forum.azimuthproject.org/discussion/2151)

[Next](https://forum.azimuthproject.org/discussion/2153)