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 prototypical example of Koszul duality was introduced by Joseph Bernstein, Israel Gelfand, and Sergei Gelfand,.^[3] It establishes a duality between the derived category of a symmetric algebra and that of an exterior algebra, as well as the BGG correspondence, which links the stable category of finite-dimensional graded modules over an exterior algebra to the bounded derived category of coherent sheaves on projective space. The importance of the notion rests on the suspicion that Koszul duality seems quite ubiquitous in nature.^{[citation needed]}