Effective codescent morphisms of $n$-quasigroups and $n$-loops
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914731836571648 |
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| author | Zangurashvili, Dali |
| author_facet | Zangurashvili, Dali |
| contents | Effective codescent morphisms of $n$-quasigroups and of $n$-loops are characterized. To this end, it is proved that, for any $n\geq 1$, every codescent morphism of $n$-quasigroups (resp. $n$-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 $n$-quasigroups (resp. $n$-loops) have unique normal forms, and that the varieties of $n$-quasigroups and $n$-loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_19187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective codescent morphisms of $n$-quasigroups and $n$-loops Zangurashvili, Dali Group Theory Category Theory 18E50, 18C20, 20N15, 20N05, 08B25, 68Q42 Effective codescent morphisms of $n$-quasigroups and of $n$-loops are characterized. To this end, it is proved that, for any $n\geq 1$, every codescent morphism of $n$-quasigroups (resp. $n$-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 $n$-quasigroups (resp. $n$-loops) have unique normal forms, and that the varieties of $n$-quasigroups and $n$-loops satisfy the strong amalgamation property. The latter two statements generalize the corresponding old results on quasigroups and loops by Evans. |
| title | Effective codescent morphisms of $n$-quasigroups and $n$-loops |
| topic | Group Theory Category Theory 18E50, 18C20, 20N15, 20N05, 08B25, 68Q42 |
| url | https://arxiv.org/abs/2403.19187 |