Completeness of the Category of Rack Crossed Modules
Authors : Hatice Gülsün Akay, Ibrahim Ilker Akça
Pages : 56-68
Doi:10.54286/ikjm.1199290
View : 11 | Download : 5
Publication Date : 2022-12-31
Article Type : Research
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