The conception of crossed modules was first expressed by Whitehead when he was working on combinatorial theory. This concept has many uses in various fields, such as category theory, algebra, and k-theory. Moreover, one of the equations that plays a very important role in mathematical problems is the Yang-Baxter equation. In fact, although it doesn't seem like it, these equations play an effective role in studies such as particle physics, statistical mechanics, quantum field theory, and quantum groups. We use crossed modules to solve them. In crossed modules, the Actor was defined by Alp. Nilpotent, Solvable, $n$-Complete, and Representations of crossed modules were studied by Dehghanizadeh and Davvaz. In studies of group theory, a simplicial group is an object. Davvaz and Alp studied simplicial polygroups, and the generalized Moore complexes. They proved the existence of a functor from the category cat$^1$-polygroups to the category of groups and, furthermore, conversely. In this paper, we provide simplicity-crossed polymodules and some of their properties. We have also presented a simple crossed polymodules theorem.

Keywords:
## Crossed module, Crossed polymodule Combinatorial homotopy,

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Bibtex | @araştırma makalesi { jnrs1293319, journal = {Journal of New Results in Science}, issn = {1304-7981}, address = {}, publisher = {Tokat Gaziosmanpaşa Üniversitesi}, year = {2023}, volume = {12}, number = {2}, pages = {86 - 96}, title = {On the simplicity crossed polymodules}, key = {cite}, author = {Dehghanizadeh, Mohammad Ali} } |

APA | Dehghanizadeh, M. A. (2023). On the simplicity crossed polymodules . Journal of New Results in Science , 12 (2) , 86-96 . |

MLA | Dehghanizadeh, M. A. "On the simplicity crossed polymodules" . Journal of New Results in Science 12 (2023 ): 86-96 < |

Chicago | Dehghanizadeh, M. A. "On the simplicity crossed polymodules". Journal of New Results in Science 12 (2023 ): 86-96 |

RIS | TY - JOUR T1 - On the simplicity crossed polymodules AU - Mohammad AliDehghanizadeh Y1 - 2023 PY - 2023 N1 - DO - T2 - Journal of New Results in Science JF - Journal JO - JOR SP - 86 EP - 96 VL - 12 IS - 2 SN - 1304-7981- M3 - UR - Y2 - 2023 ER - |

EndNote | %0 Journal of New Results in Science On the simplicity crossed polymodules %A Mohammad Ali Dehghanizadeh %T On the simplicity crossed polymodules %D 2023 %J Journal of New Results in Science %P 1304-7981- %V 12 %N 2 %R %U |

ISNAD | Dehghanizadeh, Mohammad Ali . "On the simplicity crossed polymodules". Journal of New Results in Science 12 / 2 (Ağustos 2023): 86-96 . |

AMA | Dehghanizadeh M. A. On the simplicity crossed polymodules. JNRS. 2023; 12(2): 86-96. |

Vancouver | Dehghanizadeh M. A. On the simplicity crossed polymodules. Journal of New Results in Science. 2023; 12(2): 86-96. |

IEEE | M. A. Dehghanizadeh , "On the simplicity crossed polymodules", , c. 12, sayı. 2, ss. 86-96, Ağu. 2023 |

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