  We prove that the factorization homologies of a scheme with coefficients in
truncated polynomial algebras compute the cohomologies of its generalized
configuration spaces. Using Koszul duality between commutative algebras and Lie
algebras, we obtain new expressions for the cohomologies of the latter. As a
consequence, we obtain a uniform and conceptual approach for treating
homological stability, homological densities, and arithmetic densities of
generalized configuration spaces. Our results categorify, generalize, and in
fact provide a conceptual understanding of the coincidences appearing in the
work of Farb--Wolfson--Wood. Our computation of the stable homological
densities also yields rational homotopy types which answer a question posed by
Vakil--Wood. Our approach hinges on the study of homological stability of
cohomological Chevalley complexes, which is of independent interest.
