An abelian category of motivic sheaves

A category of motivic “sheaves” is constructed over a variety in characteristic 0 using Nori’s method. Although the relationship with many alternative constructions remains to be clarified, it does have many of the properties one expects. For example, it is abelian and has Betti, Hodge and ℓℓ-adic realizations, and it has a Tannakian subcategory of motivic local systems.