Let $S,T$ be simplicial sets. Suppose $f:S\rightarrow T, f':S'\rightarrow T'$ are both categorical equivalence of simplicial sets. In the sense of Lurie, i.e. the induced map $\mathfrak{C}$ is an equivalence of simplicial categories.
Then is it true that $ S \times S' \rightarrow T \times T'$ is also a categorical equivalence?