Let
be a commutative
noetherian ring and
a
finitely generated
-module.
In this paper, we reconstruct
from its Koszul homology with respect to a suitable sequence of elements of
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
-modules,
its bounded derived category and the singularity category of
.
