A Comparison of Categories of Nori Motivic Sheaves

Abstract

We show that two different possible theories of Nori motivic sheaves, introduced by Ivorra--Morel and by Ayoub, respectively, are canonically equivalent. The proof of this result, which exploits the six functor formalism systematically, is based on the Tannakian theory of motivic local systems. As a consequence, we obtain a system of realization functors of Voevodsky motivic sheaves into Nori motivic sheaves compatible with the six operations, previously constructed by Tubach using different methods.