Differential graded Koszul duality: an introductory survey

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.

arXiv commentLaTeX 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

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Cited by in corpus (3)

• Fp-projective periodicity
• Coderived and contraderived categories of locally presentable abelian DG-categories
• Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors