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.

Fibered aspects of Yoneda's regular span / A.S. Cigoli, S. Mantovani, G. Metere, E.M. Vitale. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 360(2020 Jan 22), pp. 106899.1-106899.62. [10.1016/j.aim.2019.106899]

Fibered aspects of Yoneda's regular span

Mantovani S.;
2020-01-22

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.
Cohomology; Crossed extension; Fibration; Regular span
Settore MAT/02 - Algebra
Settore MAT/04 - Matematiche Complementari
12-nov-2019
ADVANCES IN MATHEMATICS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/721000
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