The tilting-cotilting correspondence

Leonid Positselski, Jan Stovicek

Published 2017-10-05Version 1

To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we construct an equivalence between the (conventional or absolute) derived categories of A and B. In the case of a big n-tilting module or, more generally, a big n-tilting object in a locally finitely presentable Grothendieck abelian category, we show that the tilting heart is the abelian category of contramodules over a topological ring.