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Horizontal Composition**

Given three categories \(\mathcal{A},\:\mathcal{B},\:\mathcal{C}\), pairs of parallel functors \(F,G:\mathcal{A}\to\mathcal{B}\) and \(H,K:\mathcal{B}\to\mathcal{C}\) and two natural transformations \(\eta:F\Rightarrow G\), \(\xi:H\Rightarrow K\), their horizontal composition is the natural transformation \((\xi*\eta):H\circ F\Rightarrow K\circ G\) given by \((\xi*\eta)_x=\xi_{G(x)}\circ H(\eta_x):HF(x)\to KG(x)\).