Let $ \mathscr{A} $ and $ \mathscr{B} $ be categories. A natural isomorphism between functors from $ \mathscr{A} $ to $ \mathscr{B} $ is an isomorphism in $ \ftrcat{\mathscr{A}}{\mathscr{B}} $ . An equivalent form of the definition is often useful: Lemma: Let $ \xymatrix@1{\mathscr{A}\rtwocell^F_G{\alpha} &\mathscr{B}} $ be a natural transformation.