6533b861fe1ef96bd12c4542
RESEARCH PRODUCT
Fibered aspects of Yoneda's regular span
Enrico VitaleSandra MantovaniAlan S. CigoliAlan S. CigoliGiuseppe Meteresubject
Pure mathematicsSpan (category theory)FibrationAlgebraic structureGeneral MathematicsCohomology; Crossed extension; Fibration; Regular spanFibered knot01 natural sciencesCohomologyMorphismMathematics::Category Theory0103 physical sciencesFOS: MathematicsClassification theoremCategory Theory (math.CT)0101 mathematicsMathematicsCrossed extension010102 general mathematicsFibrationMathematics - Category TheoryMathematics - Rings and AlgebrasSettore MAT/02 - AlgebraTransfer (group theory)Regular spanRings and Algebras (math.RA)Product (mathematics)010307 mathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-06-06 |