Completeness of the Category of Rack Crossed Modules

Year 2022, Volume: 4 Issue: 2, 56 - 68, 31.12.2022

Hatice Gülsün Akay , İbrahim İlker Akça

https://doi.org/10.54286/ikjm.1199290

Cited By: 1

Abstract

In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. In other words, we construct the product, pullback and equalizer objects in the category of crossed modules of racks. We therefore unify the group-theoretical analogy of the completeness property in the sense of the functor $\mathbf{Conj \colon Grp \to Rack} $.

Keywords

Crossed module, limit, rack

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