  We introduce polyhedral products in an $\infty$-categorical setting. We
generalize a splitting result by Bahri, Bendersky, Cohen, and Gitler that
determines the stable homotopy type of the a polyhedral product. We also
introduce a motivic refinement of moment-angle complexes and use the splitting
result to compute cellular $\mathbb{A}^1$-homology, and $\mathbb{A}^1$-Euler
characteristics.
