In this paper, we define a generalized notion of semidirect hyperproduct of polygroups and use that to introduce a pushout construction for crossed polymodules. 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 of the crossed polysquare version of homotopy cokernels.
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Dehghanizadeh et al. (2025) studied this question.
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