Does full imply faithful?
Algebraic Geometry
2013-12-10 v2 Category Theory
Abstract
We study full exact functors between triangulated categories. With some hypotheses on the source category we prove that it admits an orthogonal decomposition into two pieces such that the functor restricted to one of them is zero while the restriction to the other is faithful. In particular, if the source category is either the category of perfect complexes or the bounded derived category of coherent sheaves on a noetherian scheme supported on a closed connected subscheme, then any non-trivial exact full functor is faithful as well. Finally we show that removing the noetherian hypothesis this result is not true.
Cite
@article{arxiv.1101.5931,
title = {Does full imply faithful?},
author = {Alberto Canonaco and Dmitri Orlov and Paolo Stellari},
journal= {arXiv preprint arXiv:1101.5931},
year = {2013}
}
Comments
12 pages. Minor changes. Final version to appear in J. Noncommut. Geom