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Abstract: The study of the bounded derived category of coherent sheaves on a smooth projective variety is a central topic in algebraic geometry. Almost all the functors arising from geometric constructions are of Fourier-Mukai type, namely they can be described by an object in the derived category of a product. In this setting, Orlov proved in 1996 that every exact fully faithful functor with adjoints is of FM type. Since then, this result has been further generalized and a useful tool is to enhance the triangulated structure on the derived category to a dg category.