Search results for "Classification theorem"
showing 2 items of 2 documents
The classification of 4-dimensional homogeneous D'Atri spaces revisited
2007
Abstract In this short note we correct the (incomplete) classification theorem from [F. Podesta, A. Spiro, Four-dimensional Einstein-like manifolds and curvature homogeneity, Geom. Dedicata 54 (1995) 225–243], we improve a result from [P. Bueken, L. Vanhecke, Three- and four-dimensional Einstein-like manifolds and homogeneity, Geom. Dedicata 75 (1999) 123–136] and we announce the final solution of the classification problem for 4-dimensional homogeneous D'Atri spaces.
Fibered aspects of Yoneda's regular span
2018
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 $Pr_0 \colon \mathcal{A} \times \mathcal{B} \to \mathcal{A}$ i…