Affine mobi spaces. (English) Zbl 1502.18018
The authors’ summary says: “The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spaces with geodesic paths. In this paper we analyse the particular case of affine mobi spaces and show that there is an isomorphism of categories between modules over unitary rings with 1/2 and pointed affine mobi spaces over mobi algebras with 2.”
In fact the paper is closely related to its two predecessors by the same authors (see [J. P. Fatelo and N. Martins-Ferreira, Commun. Algebra 47, No. 3, 1197–1214 (2019; Zbl 1439.08004); Cah. Topol. Géom. Différ. Catég. 63, No. 1, 59–88 (2022; Zbl 1486.08003)]; the Zbl review of the last cited by K. Kearnes is especially useful). The main novelty in the present paper is indeed:
“Theorem 4.5 There is an isomorphism of categories between modules over a ring with 1/2 and pointed affine mobi spaces over a mobi algebra with 2.”
Note: The ring with 1/2 and the mobi algebra with 2 involved here should correspond to each other via a previously established isomorphism between the categories of rings with 1/2 and mobi algebras with 2.
In fact the paper is closely related to its two predecessors by the same authors (see [J. P. Fatelo and N. Martins-Ferreira, Commun. Algebra 47, No. 3, 1197–1214 (2019; Zbl 1439.08004); Cah. Topol. Géom. Différ. Catég. 63, No. 1, 59–88 (2022; Zbl 1486.08003)]; the Zbl review of the last cited by K. Kearnes is especially useful). The main novelty in the present paper is indeed:
“Theorem 4.5 There is an isomorphism of categories between modules over a ring with 1/2 and pointed affine mobi spaces over a mobi algebra with 2.”
Note: The ring with 1/2 and the mobi algebra with 2 involved here should correspond to each other via a previously established isomorphism between the categories of rings with 1/2 and mobi algebras with 2.
Reviewer: George Janelidze (Cape Town)
MSC:
| 18E05 | Preadditive, additive categories |
| 08C15 | Quasivarieties |
| 08A62 | Finitary algebras |
| 16D10 | General module theory in associative algebras |
References:
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| [5] | Fatelo, JP; Martins-Ferreira, N., Internal monoids and groups in the category of commutative cancellative medial magmas, Port. Math., 73, 3, 219-245 (2016) · Zbl 1358.08002 · doi:10.4171/PM/1986 |
| [6] | Fatelo, JP; Martins-Ferreira, N., Mobi algebra as an abstraction to the unit interval and its comparison to rings, Commun. Algebra, 47, 3, 1197-1214 (2019) · Zbl 1439.08004 · doi:10.1080/00927872.2018.1501575 |
| [7] | Fatelo, JP; Martins-Ferreira, N., Mobi spaces and geodesics for the N-sphere, Cah. Topol. Géom. Différ. Catég., 63, 1, 59-88 (2022) · Zbl 1486.08003 |
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