# Definition:Vertical Composition of Natural Transformations

## Definition

Let $C$ and $D$ be categories.

Let $F,G,H : C \to D$ be covariant functors.

Let $\eta : F \to G$ and $\xi : G \to H$ be natural transformations.

The vertical composition of $\eta$ and $\xi$ is the natural transformation $\xi \circ \eta : F \Rightarrow H$ with $(\xi \circ \eta)_A = \xi_A \circ \eta_A$ for $A\in C$.