\begin{definition}[Definition:Composition of Functors]
Let $\mathbf C, \mathbf D$ and $\mathbf E$ be metacategories.
Let $F: \mathbf C \to \mathbf D$ and $G: \mathbf D \to \mathbf E$ be (covariant) functors.
The '''composition of $G$ with $F$''' is the functor $GF: \mathbf C \to \mathbf E$ defined by:
:For all objects $C$ of $\mathbf C$: $\hskip{2.9cm} GF \left({C}\right) := G \left({FC}\right)$
:For all morphisms $f: C_1 \to C_2$ of $\mathbf C$: $\quad GF \left({f}\right) := G \left({Ff}\right)$
$GF$ is said to be a '''composite functor'''.
\end{definition}