19/04/12 22:36:02.93 wJTveQLJ.net
Let SmProj C corSmProj^{cor}_\mathbf{C} denote the category of algebraic correspondences of smooth projective algebraic varieties over the complex numbers.
The canonical functor
SmProj cor→HS pure SmProj^{cor} \to HS^{pure}
to the category of rational pure Hodge structures, given by taking rational Betti cohomology, is fully faithful.