# Generators and representability of functors in commutative and noncommutative geometry

@article{Bondal2002GeneratorsAR, title={Generators and representability of functors in commutative and noncommutative geometry}, author={Alexei Bondal and Michel van den Bergh}, journal={arXiv: Algebraic Geometry}, year={2002} }

We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence of a strong generator. We prove that the bounded derived categories of coherent sheaves on smooth proper commutative and noncommutative varieties have strong generators, hence saturated. In contrast the similar category for a smooth compact analytic surface…

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