自然変換の定義
Let $ F,G:\mathfrak{C}\to\mathfrak{D} be functors between categories C and D. A natural transformation $ \Phi from F to G consists of a family $ \Phi_C:F(\mathfrak{C})\to G(\mathfrak{C}) of morphisms in $ \mathfrak{D} which are indexed by the objects C of $ \mathfrak{C} so that, for each morphism $ f:C\to D between objects in $ \mathfrak{C}, the equality
$ G(f) \circ \Phi_C=\Phi_D \circ F(f):F(C)\to G(D)
holds. The elements $ \Phi_C are called the components of the natural transformation.
If all the components $ \Phi_C are isomorphisms in $ \mathfrak{D}, then $ \Phi is called a natural isomorphism between F and G. In this case, one writes $ \Phi:F \simeq G.
さっぱりわからんnishio.icon