natural in Y means that for every f:Y \rightarrow Y', \alpha:\mathcal{D}(FX,Y) \rightarrow \mathcal{C}(X,GY) composed with \mathcal{C}(X,Gf):\mathcal{C}(X,GY) \rightarrow \mathcal{C}(X,GY') commutes with \mathcal{D}(FX,f):\mathcal{D}(FX,Y) \rightarrow \mathcal{D}(FX,Y') composed with \alpha:\mathcal{D}(FX,Y') \rightarrow \mathcal{C}(X,GY').