φ[C2] ∘ η[C2] ∘ G(f) = J(f) ∘ φ[C1] ∘ η[C1]
</pre>
-Hence, we can define <code>(φ -v- η)[x]</code> as: <code>φ[x] ∘ η[x]</code> and rely on it to satisfy the constraints for a natural transformation from `G` to `J`:
+Hence, we can define <code>(φ -v- η)[\_]</code> as: <code>φ[\_] ∘ η[\_]</code> and rely on it to satisfy the constraints for a natural transformation from `G` to `J`:
<pre>
(φ -v- η)[C2] ∘ G(f) = J(f) ∘ (φ -v- η)[C1]
<pre>
(φ -h- η)[C1] = L(η[C1]) ∘ ψ[G(C1)]
- = ψ[H(C1)] ∘ K(η[C1])
+ = ψ[H(C1)] ∘ K(η[C1])
</pre>
Horizontal composition is also associative, and has the same identity as vertical composition.