Completeness of the Category of Rack Crossed Modules

Author:

GÜLSÜN AKAY Hatice1ORCID,AKÇA İbrahim İlker1

Affiliation:

1. ESKISEHIR OSMANGAZI UNIVERSITY

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} $.

Publisher

Ikonion Journal of Mathematics

Reference13 articles.

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2. Alp, M. (2006) Pullbacks of crossed modules and cat-1 commutative algebras, Turkish Journal of Mathematics, 30:237-246.

3. Brown, R., Wensley, C.D. (1995) On infinite induced crossed modules and the homotopy 2-type of mapping cones. Theory Appl. Categ., 1.

4. Crans, A.S., Wagemann, F. (2014) Crossed modules of racks. Homology Homotopy Appl., 16(2):85–106.

5. Davvaz, B., Emir, K. (2020) On morphisms of crossed polymodules. Notices of AMS, 9(1):95-103.

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