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Fourier-Mukai Transforms in Algebraic Geometry$
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D. Huybrechts

Print publication date: 2006

Print ISBN-13: 9780199296866

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199296866.001.0001

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Triangulated Categories

Triangulated Categories

(p.1) 1 Triangulated Categories
Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Oxford University Press

Reviewing the basic notions of additive and abelian categories, left and right adjoint functors, and Serre functors, this chapter is mainly devoted to triangulated categories. In particular, criteria are established which decide when a given functor is fully-faithful or an equivalence. This is formulated in terms of spanning classes. The last section discusses exceptional objects in triangulated categories which lead naturally to the notion of orthogonal decompositions of categories.

Keywords:   abelian category, full functor, faithful functor, adjoint functor, Serre functor, equivalence, exceptional object

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