Related papers: Koszul duality for non-graded derived categories
We study a categorified generalization of Koszul duality that treats duality phenomena among monoidal categories. We establish Koszul duality results for stable monoidal infinity-categories associated with Artin algebras and related…
Let $A$ be a proper non-positive dg algebra over a field $k$. For a simple-minded collection of the finite-dimensional derived category $\mathcal{D}_{fd}(A)$, we construct a 'dual' silting object of the perfect derived category…
We prove an analogue of Koszul duality for category $\mathcal{O}$ of a reductive group $G$ in positive characteristic $\ell$ larger than 1 plus the number of roots of $G$. However there are no Koszul rings, and we do not prove an analogue…
A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then $RHom_A(?,K): D^{df}_{+}(A)^{op} \equiv…
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…
We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in…
It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…
We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a…
We use linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras studied in previous papers of the authors to give a geometric realization of the Iwahori-Matsumoto involution of…
We prove that on a certain class of smooth complex varieties (those with "affine even stratifications"), the category of mixed Hodge modules is "almost" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give…
Let p be a prime number. We compute the Yoneda extension algebra of $GL_2$ over an algebraically closed field of characteristic p by developing a theory of Koszul duality for a certain class of 2-functors, one of which controls the category…
Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the…
We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O associated to a reductive finite dimensional Lie algebra. In particular we find that, contrary to the original category O and the specific…
Generalizing Jacob Lurie's idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorization algebras. We formulate an analogue of Lurie's "nonabelian…
We prove a version of Koszul duality and the induced derived equivalence for Adams connected $A_\infty$-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the…
Generalizing a concept of Lipshitz, Ozsv\'ath and Thurs-ton from Bordered Floer homology, we define $D$-structures on algebras of unital operads, which can also be interpreted as a generalization of a seemingly unrelated concept of Getzler…
Let $S$ be an $\mathbb N$-graded Koszul Artin-Schelter regular algebra and let $\sigma$ be a graded algebra automorphism of $S$. We study the stable category of graded maximal Cohen-Macaulay modules over the trivial extension algebra…
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between…
In this paper, we define $A_{\infty}$-Koszul duals for directed $A_{\infty}$-categories in terms of twists in their $A_{\infty}$-derived categories. Then, we compute a concrete formula of $A_{\infty}$-Koszul duals for path algebras with…
In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known…