English

Effective codescent morphisms of $n$-quasigroups and $n$-loops

Group Theory 2024-03-29 v1 Category Theory

Abstract

Effective codescent morphisms of nn-quasigroups and of nn-loops are characterized. To this end, it is proved that, for any n1n\geq 1, every codescent morphism of nn-quasigroups (resp. nn-loops) is effective. This statement generalizes our earlier results on qusigroups and loops. Moreover, it is shown that the elements of the amalgamated free products of nn-quasigroups (resp. nn-loops) have unique normal forms, and that the varieties of nn-quasigroups and nn-loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans.

Keywords

Cite

@article{arxiv.2403.19187,
  title  = {Effective codescent morphisms of $n$-quasigroups and $n$-loops},
  author = {Dali Zangurashvili},
  journal= {arXiv preprint arXiv:2403.19187},
  year   = {2024}
}