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.

Cigoli A.S., Mantovani S., Metere G., & Vitale E.M. (2020). Fibered aspects of Yoneda's regular span. ADVANCES IN MATHEMATICS, 360, 1-62 [10.1016/j.aim.2019.106899].

Fibered aspects of Yoneda's regular span

Cigoli A. S.
;
Metere G.;
2020

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 MAT/02 - Algebra
Cigoli A.S., Mantovani S., Metere G., & Vitale E.M. (2020). Fibered aspects of Yoneda's regular span. ADVANCES IN MATHEMATICS, 360, 1-62 [10.1016/j.aim.2019.106899].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/425150
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