Title: The diagonal of the operahedra
Abstract: The set-theoretic diagonal of a polytope has the crippling defect of not being cellular: its image is not a union of cells. Our goal here is to develop a general theory, based on the method introduced by N. Masuda, H. Thomas, A. Tonks and B. Vallette, in order to understand and manipulate the cellular approximations of the diagonal of any polytope. This theory will allow us to tackle the problem of the cellular approximation of the diagonal of the operahedra, a family of polytopes ranging from the associahedra to the permutohedra, and which encodes homotopy operads. In this way, we obtain an explicit formula for the tensor product of two such operads, with interesting combinatorial properties
Reference: https://arxiv.org/abs/2110.14062
