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Vertical Composition**

Given three parallel functors \(F,G,H:\mathcal{C}\to\mathcal{D}\) between categories \(\mathcal{C},\:\mathcal{D}\) and two natural transformations \(\eta:F\Rightarrow G,\:\xi:G\Rightarrow H\), their vertical composition is the natural transformation \((\xi\circ\eta):F\Rightarrow H\) defined by \((\xi\circ\eta)_x=(\xi_x\circ \eta_x):F(x)\to H(x)\).