As we have said, mathematical constructions generally define objects only up to isomorphism, because frequently there is a different but equally useful representation which can be substituted. For example there are two versions of the three-fold cartesian product. Thus functors are often parametric objects and so, like objects, are intrinsically defined only up to isomorphism.
D be two parallel functors.
In this case the definition of f must be extended from base types to contexts in the same way as in the remarks after Definition 4.6.2 . Natural transformations show up even when we only set out to consider categories and functors. Let C and G be categories. The pairing operation and projection functions are as expected. For posets, vertical composition is the transitivity of the pointwise order.