We show that a categorical generalization of the the Poincar symmetry which is based on the n-crossed modules becomes natural and simple when n=3 and that the corresponding 3-form and 4-form gauge fields have to be a Dirac spinor and a Lorentz scalar, respectively. Hence by using a Poincar 4-group we naturally incorporate fermionic and scalar matter into the corresponding 4-connection. The internal symmetries can be included into the 4-group structure by using a 3-crossed module based on the group, so that for we can include the Standard Model into this categorification scheme.

中文翻译：

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标准型和4组

我们表明，当n = 3时，基于n交叉模的庞加莱对称性的分类推广变得自然而简单，并且相应的 3 型和 4 型规范场必须是狄拉克旋量和洛伦兹标量，分别。因此，通过使用 Poincar 4-群，我们自然地将费米子和标量物质合并到相应的 4-连接中。内部对称性可以通过使用基于群的 3-crossed 模块包含在 4-group 结构中，因此我们可以将标准模型包含在这个分类方案中。