Reconstruction from Koszul homology and applications to module and derived categories

Let R be a commutative noetherian ring and M a finitely generated R-module.In this paper, we reconstruct M from its Koszul homology with respect to a suitable sequence of elements of R by taking direct summands, syzygies and extensions, and count the number of those operations.Using this result, we consider generation and classification of certain subcategories of the category of finitely generated R-modules, its bounded derived category and the singularity category of R.