Contravariant Hom Functor

$$\begin{array}{rl}\text{Let }& G=\lambda X.\mathcal{C}[X,A]\\ & f:{\mathcal{C}}^{\mathrm{op}}[B,C]=\mathcal{C}[C,B]\\ & G(f):\mathcal{C}[B,A]\to \mathcal{C}[C,A]\\ & G(f)(g)=g\circ f\end{array}$$

See also