According to the prescription of functorial quantum field theory, a quantum field theory can be viewed as a monoidal functor from some monoidal category of $n$-cobordisms to some monoidal category of vector spaces (typically a category of Hilbert spaces).

Now, what does the functor category of QFTs look like? More precisely, I am having trouble even conceptualizing what "natural transformation between QFTs" would be. I am also interested in the specific case of the category of CFTs (a CFT here would be a monoidal functor from a conformal cobordism category).