On crossed polysquare version of homotopy kernels

In this paper, we introduce the notion of braiding crossed polymodule and $\Gamma$\_equivariant braided crossed polymodule of polygroups and we give some of its properties. Further we have concept Fiber hyper product. Our results extend the classical results of crossed squares to crossed polysquares. One of the main tools in the study to polygroups is the fundamental relations. Additionally, we study on crossed polysquare version of homotopy kernels.