Horizontal Linkage of Coherent Functors

Abstract

The satellite endofunctors are used to extend the definition of linkage of ideals to the linkage of totally finitely presented functors. The new notion for linkage works over a larger class of rings and is consistent with the functorial approach of encoding information about modules into the category of finitely presented functors. In the process of extending linkage, we recover the Auslander-Gruson-Jensen duality using injective resolutions of finitely presented functors. Using the satellite endofunctors we give general definitions of derived functors which do not require the existence of projective or injective objects. A general formula for calculating the defect of a totally finitely presented functor is given.