Fibered aspects of Yoneda's regular span
| Autor: | Enrico Vitale, Sandra Mantovani, Alan S. Cigoli, Giuseppe Metere |
|---|---|
| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique, Cigoli A.S., Mantovani S., Metere G., Vitale E.M. |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Span (category theory) Fibration Algebraic structure General Mathematics Cohomology Crossed extension Regular span Fibered knot 01 natural sciences Morphism Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Classification theorem Category Theory (math.CT) 0101 mathematics Mathematics 010102 general mathematics Mathematics - Category Theory Mathematics - Rings and Algebras Settore MAT/02 - Algebra Transfer (group theory) Rings and Algebras (math.RA) Product (mathematics) 010307 mathematical physics |
| Zdroj: | Advances in Mathematics, Vol. 360, p. 106899 (2020) |
| Popis: | In this paper we start by pointing out that Yoneda's notion of a regular span $S \colon \mathcal{X} \to \mathcal{A} \times \mathcal{B}$ can be interpreted as a special kind of morphism, that we call fiberwise opfibration, in the 2-category $\mathsf{Fib}(\mathcal{A})$. 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 $Pr_0 \colon \mathcal{A} \times \mathcal{B} \to \mathcal{A}$ is replaced by any split fibration over $\mathcal{A}$. 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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