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EnglishIn this paper we start by pointing out that Yoneda's notion of a regular span S:X→A×B can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category Fib(A). We study the relationship between these notions and those of internal opfibration and two-sided fibration. This fibrational point of view makes it possible to interpret Yoneda's Classification Theorem given in his 1960 paper as the result of a canonical factorization, and to extend it to a non-symmetric situation, where the fibration given by the product projection Pr0:A×B→A is replaced by any split fibration over A. This new setting allows us to transfer Yoneda's theory of extensions to the non-additive analog given by crossed extensions for the cases of groups and other algebraic structures.
Cigoli A.S., Mantovani S., Metere G., & Vitale E.M. (2020). Fibered aspects of Yoneda's regular span. ADVANCES IN MATHEMATICS, 360, 1-62.
| Data di pubblicazione: | 2020 |
| Titolo: | Fibered aspects of Yoneda's regular span |
| Autori: | |
| Citazione: | Cigoli A.S., Mantovani S., Metere G., & Vitale E.M. (2020). Fibered aspects of Yoneda's regular span. ADVANCES IN MATHEMATICS, 360, 1-62. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aim.2019.106899 |
| Abstract: | In this paper we start by pointing out that Yoneda's notion of a regular span S:X→A×B can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category Fib(A). We study the relationship between these notions and those of internal opfibration and two-sided fibration. This fibrational point of view makes it possible to interpret Yoneda's Classification Theorem given in his 1960 paper as the result of a canonical factorization, and to extend it to a non-symmetric situation, where the fibration given by the product projection Pr0:A×B→A is replaced by any split fibration over A. This new setting allows us to transfer Yoneda's theory of extensions to the non-additive analog given by crossed extensions for the cases of groups and other algebraic structures. |
| Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 1806.02376.pdf | pre-print | Pre-print | Open Access Visualizza/Apri | |
| 1-s2.0-S0001870819305146-main.pdf | Versione Editoriale | Administrator Richiedi una copia |
http://hdl.handle.net/10447/425150
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