Computing 3-Dimensional Groups : Crossed Squares and Cat$^2$-Groups

Zekeriya Arvasi; Alper Odabaş; Christopher D. Wensley

Computing 3-Dimensional Groups : Crossed Squares and Cat$^2$-Groups

Algebraic Topology 2019-12-02 v1 Category Theory

Authors: Zekeriya Arvasi , Alper Odabaş , Christopher D. Wensley

Abstract

The category $\mathbf{XSq}$ of crossed squares is equivalent to the category $\mathbf{Cat2}$ of cat $^2$ -groups. Functions for computing with these structures have been developed in the package $\mathsf{XMod}$ written using the $\mathsf{GAP}$ computational discrete algebra programming language. This paper includes details of the algorithms used. It contains tables listing the $1,000$ isomorphism classes of cat $^2$ -groups on groups of order at most $30$ .

Cite

@article{arxiv.1911.12799,
  title  = {Computing 3-Dimensional Groups : Crossed Squares and Cat$^2$-Groups},
  author = {Zekeriya Arvasi and Alper Odabaş and Christopher D. Wensley},
  journal= {arXiv preprint arXiv:1911.12799},
  year   = {2019}
}

Comments

15 pages, xypic

Computing 3-Dimensional Groups : Crossed Squares and Cat$^2$-Groups

Abstract

Cite

Comments

Related papers