Search results for "Fibred category"
showing 2 items of 2 documents
Bourn-normal monomorphisms in regular Mal’tsev categories
2017
Normal monomorphisms in the sense of Bourn describe the equivalence classes of an internal equivalence relation. Although the definition is given in the fairly general setting of a category with finite limits, later investigations on this subject often focus on protomodular settings, where normality becomes a property. This paper clarifies the connections between internal equivalence relations and Bourn-normal monomorphisms in regular Mal’tesv categories with pushouts of split monomorphisms along arbitrary morphisms, whereas a full description is achieved for quasi-pointed regular Mal’tsev categories with pushouts of split monomorphisms along arbitrary morphisms.
Beilinson Motives and Algebraic K-Theory
2019
Section 12 is a recollection on the basic results of stable homotopy theory of schemes, after Morel and Voevodsky. In particular, we recall the theory of orientations in a motivic cohomology theory. Section 13 is a recollection of the fundamental results on algebraic K-theory which we translate into results within stable homotopy theory of schemes. In particular, Quillen’s localization theorem is seen as an absolute purity theory for the K-theory spectrum. In Section 14, we introduce the fibred category of Beilinson motives as an appropriate Verdier quotient of the motivic stable homotopy category. Using the Adams filtration on K-theory, we prove that Beilinson motives have the properties o…