Polyhedral products in abstract and motivic homotopy theory

We introduce polyhedral products in an $\mathrm{\infty }$-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.