The Nori fundamental gerbe of a fibered category

We extend Nori's theory of the fundamental group scheme to a theory of the fundamental gerbe, which applies to schemes, algebraic stacks, and more general fibered categories, even in absence of a rational point. We give a tannakian interpretation of the fundamental gerbe in terms of essentially finite bundles, extending Nori's correspondence for complete varieties with a rational point. We also show how our formalism allows a natural formulation of Grothendieck's section conjecture in arbitrary characteristic.