Koszul duality for dg-categories and infinity-categories

Andrey Lazarev (Lancaster University, UK)

08-Oct-2020, 11:00-12:00 (3 years ago)

Abstract: Differential graded (dg) Koszul duality is a certain adjunction between the category of dg algebras and conilpotent dg coalgebras that becomes an equivalence on the levels of homotopy categories. More precisely, this adjunction is a Quillen equivalence of the corresponding closed model categories. Various versions of this result exist and play important roles in rational homotopy theory, deformation theory, representation theory and other related fields. We extend it to a Quillen equivalence between dg categories (generalizing dg algebras) and a class of dg coalgebras, more general than conilpotent ones. As applications we describe explicitly and conceptually Lurie’s dg nerve functor as well as its adjoint and characterize derived categories of (\infty,1)-categories as derived categories of comodules over simplicial chain coalgebras.(joint work with J. Holstein)

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )


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