Koszul duality

In mathematics, Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras, abstract algebras (semisimple algebra)^[1] and topology (e.g., equivariant cohomology^[2]). The prototype example is the BGG correspondence, due to Joseph Bernstein, Israel Gelfand, and Sergei Gelfand,.^[3] It is a duality between the derived category of a symmetric algebra and that of an exterior algebra. The importance of the notion rests on the suspicion that Koszul duality seems quite ubiquitous in nature.^{[citation needed]}