This offers two different perspectives on associative algebras: homological invariants are “abelian” (i. e. arise when one works with an additive category, e.g. chain complexes of modules over a ring), while homotopical invariants are “non-abelian” (i. e. arise from non-additive categories, like the category of all DGAs differential graded associative algebras). However, these two perspectives are closely related, and it is often possible to recover homological information from the homotopical one, and the other way round. For experts in homotopical algebra on a larger scale (beyond the associative ring theory), this philosophy is already present in works of Stasheff and Hinich on homotopy algebras.

Closely related to DGAs