hom object

Let \((\mathcal{V}, \otimes_{\mathcal{V}}, \mathds{1}_{\mathcal{V}})\) be a monoidal category and \(\mathcal{C}\) an \(\mathcal{V}\)-enriched category Then for \(C_1,C_2 \in \mathcal{C}\) the hom object is defined as

\begin{align*} \mathrm{Hom}_{\mathcal{C}}^{\mathcal{V}}(C_1,C_2) \end{align*}