To transfer a tensored and cotensored simplicially enriched structure from a category $\mathcal{C}$ to $(\mathcal{C}\downarrow Z)$, we define $(X\to Z)\otimes K$ by the composite $(X\otimes K \to X \otimes \{0\} \to Z)$ and $(X\to Z)^K$ by a pullback of $X^K\to Z^K$ and $Z^{\{0\}} \to Z^K$. I just need to know in what textbook it is written down for a bibliographical reference. It is also not in Overcategories and undercategories of cofibrantly generated model categories.