English

Differential graded Koszul duality: an introductory survey

Category Theory 2023-08-04 v5 History and Overview Rings and Algebras

Abstract

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG-algebras and curved DG-coalgebras, as well as the triality between DG-modules, CDG-comodules, and CDG-contramodules. Some personal reminiscences are included as a part of historical discussion.

Cite

@article{arxiv.2207.07063,
  title  = {Differential graded Koszul duality: an introductory survey},
  author = {Leonid Positselski},
  journal= {arXiv preprint arXiv:2207.07063},
  year   = {2023}
}

Comments

LaTeX 2e with xy-pic, graphicx.sty, and one mathb symbol; 96 pages, 2 commutative diagrams; v.2: Sections 8 and 9 added -- this is intended as a complete version; v.3: new Remark 7.14 inserted, Subsections 4.5 and 9.8 added, other small additions; v.4: Example 2.3, Remark 3.5, and Propositions 3.4, 6.1, and 6.3 inserted; v.5: several misprints corrected, two references updated

R2 v1 2026-06-25T00:55:25.512Z