Figure 4.

What is a natural transformation? (a) Category C (consisting of objects X and Y and an arrow f) is mapped into category D by two functors F and G. Each functor preserves the structure of category C in D (e.g. F(f):F(X) → F(Y), G(f):G(X) → G(Y)). Natural transformation t maps functor F into G while preserving its structure. t can be considered as a family of arrows in category D, such as tX and tY. Each arrow is specified by an object in the original category C, such as tX, which maps an object F(X) to G(X) in category D. b) Visualizing t as a family of arrows in the destination category D