Fibered aspects of Yoneda's regular span

Giuseppe Metere, Alan S. Cigoli, Enrico M. Vitale, Sandra Mantovani

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1 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)1-62
Numero di pagine63
RivistaAdvances in Mathematics
Volume360
Stato di pubblicazionePublished - 2020

All Science Journal Classification (ASJC) codes

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