Definition 14.17.1. Let $\mathcal{C}$ be a category such that the coproduct of any two objects exists. Let $U$ be a simplicial set, with $U_ n$ finite nonempty for all $n \geq 0$. Let $V$ be a simplicial object of $\mathcal{C}$. We denote *$\mathop{\mathrm{Hom}}\nolimits (U, V)$* any simplicial object of $\mathcal{C}$ such that

functorially in the simplicial object $W$ of $\mathcal{C}$.

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