A Morphism between Functors

Let $F,G: \mathcal{C} \to \mathcal{D}$ be Functors. A natural transformation $t: F \Rightarrow G$ is a family of $\mathcal{D}$-morphisms

$t_A : FA \to GA$

indexed by objects $A$ of $\mathcal{C}$ such that for all $f:A \to B$,

If each $t_A$ is an Isomorphism, we say that $t$ is a Natural isomorphism.

Meaning of "natural transformation/isomorphism in variables" when not specifying functor explicitely

Notes

Vertical and horizontal composition of natural transformations