Korean J. Math. Vol. 26 No. 3 (2018) pp.439-458
DOI: https://doi.org/10.11568/kjm.2018.26.3.439

Derived crossed modules

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Published: Sep 30, 2018
Keywords:
Homotopy, crossed module, internal category, group with operations.
Mathematics Subject Classification:
55U35, 18D35, 20L05, 18A23.

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Tunçar Şahan
Department of Mathematics Aksaray University Aksaray 68100, Turkey

Abstract

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\mathsf{C}$ of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in $\mathsf{C}$. Further, we characterize the derivations of crossed modules in a category $\mathsf{C}$ and obtain new crossed modules using regular derivations of old one.


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References

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