Polyhedral products in abstract and motivic homotopy theory

Abstract

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.

v2. Corrected an error in Example 7.13 and minor typos