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If F is a functor linking category C to category D, and G is a functor linking category C to category E,(and assuming that both functors are bijections), does this imply that there is a unique natural transformation from functor F to functor G?

A natural transformation is between functors with the same domain and the same codomain, so that's where it already goes wrong?Sjoerd Visscher
Thanks. Didn't realize that.DMJ