# Crossed modules with action

### Abstract

UDC 512.5

Following the idea of a group with action, in a higher dimension, we consider crossed modules with a given crossed-module action upon itself. A category of these objects $\mathbf{XMod}^*$ is given by replacing the set of morphisms in the category $\mathbf{Gr}^*$ of groups with action by the set of a modified form of $\varphi$-crossed homomorphisms. Moreover, the connections of $\mathbf{XMod}^*$ with some other known categories, such as $\mathbf{Gr}^*$ and $\mathbf{XMod},$ are given by describing some related functors.

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*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 76, no. 4, Apr. 2024, pp. 581 -98, doi:10.3842/umzh.v74i4.7371.

Copyright (c) 2024 Selim Çetin

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