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Hom Set**

Given a category \(\mathcal{C}\) and a pair of objects \(x,y\in\mathcal{C}_0\), the 'hom set' \(\mathcal{C}(x,y)=\mathrm{Hom}_\mathcal{C}(x,y)\) is the collection of all arrows from \(x\) to \(y\), i.e. \(\{f\in\mathcal{C}_1|\mathrm{dom}(f)=x\land\mathrm{cod}(f)=y\}\).