Homological stability and densities of generalized configuration spaces

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