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Higher-dimensional self-acting groups: From crossed modules to internal categories
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DOI：10.1515/gmj-2026-2015.png)
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Abstract
En 中文
In many algebraic settings, the categories of crossed modules, cat 1 {\mathrm{cat}<^>{1}} -objects, and internal categories are known to be categorically equivalent. In this paper, we develop this correspondence in the category in self-acting groups. We first construct crossed modules, cat 1 {\mathrm{cat}<^>{1}} -objects, and internal categories in this context and establish their fundamental structural properties. We then prove that the categories of these three types of objects in the category of self-acting groups are equivalent. This provides a unified categorical framework for interpreting higher-dimensional algebraic structures arising from self-actions.
Keywords:
Self-acting groups
crossed modules
internal categories