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 $\paren {\xi \circ \eta}_A = \xi_A \circ \eta_A$ for $A \in C$.

Also see

 * Vertical Composition of Natural Transformations is Natural Transformation
 * Definition:Functor Category
 * Definition:Horizontal Composition of Natural Transformations