Reflexivity in Derived Categories
K-Theory and Homology
2009-05-20 v2 Category Theory
Abstract
An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. We describe the reflexive complexes and interpret the achieved results in terms of objects of the initial abelian categories. In particular we prove that, for functors of any finite cohomological dimension, the objects of the initial abelian categories which are reflexive as stalk complexes form the largest class where a Cotilting Theorem in the sense of Colby and Fuller works.
Cite
@article{arxiv.0705.2537,
title = {Reflexivity in Derived Categories},
author = {Francesca Mantese and Alberto Tonolo},
journal= {arXiv preprint arXiv:0705.2537},
year = {2009}
}