Journal of Noncommutative Geometry


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Volume 7, Issue 2, 2013, pp. 357–371
DOI: 10.4171/JNCG/120

Published online: 2013-05-06

Does full imply faithful?

Alberto Canonaco[1], Dmitri Orlov[2] and Paolo Stellari[3]

(1) Università di Pavia, Italy
(2) Steklov Mathematical Institute, Moscow, Russia
(3) Università di Milano, Italy

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.

Keywords: Derived categories, triangulated categories, exact functors

Canonaco Alberto, Orlov Dmitri, Stellari Paolo: Does full imply faithful?. J. Noncommut. Geom. 7 (2013), 357-371. doi: 10.4171/JNCG/120