Effective codescent morphisms of $n$-quasigroups and $n$-loops
Group Theory
2024-03-29 v1 Category Theory
Abstract
Effective codescent morphisms of -quasigroups and of -loops are characterized. To this end, it is proved that, for any , every codescent morphism of -quasigroups (resp. -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 -quasigroups (resp. -loops) have unique normal forms, and that the varieties of -quasigroups and -loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans.
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}
}