Related papers: A construction of quotient A_infinity-categories

To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we…

Consider a Grothendieck category $\mathcal{G}$ along with a choice of generator $G$, or equivalently a generating set $\{G_i\}$. We introduce the derived category $\mathcal{D}(G)$, which kills all $G$-acyclic complexes, by putting a…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

We show that for the path algebra $A$ of an acyclic quiver, the singularity category of the derived category $\mathsf{D}^{\rm b}(\mathsf{mod}\,A)$ is triangle equivalent to the derived category of the functor category of…

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…

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,…

To any affine scheme with a $\mathbb{G}_m$-action, we provide a Bousfield colocalization on the equivariant derived category of modules by constructing, via homotopical methods, an idempotent integral kernel. This endows the equivariant…

We provide a universal construction of the category of finite-dimensional C*-algebras and completely positive trace-nonincreasing maps from the rig category of finite-dimensional Hilbert spaces and unitaries. This construction, which can be…

Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra $A$ with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk_2(\mp(A))$ of $\mk^b(\mp(A))$ in term of constructible…

Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which…

We relate a construction of Kadeishvili's establishing an A-infinity-structure on the homology of a differential graded algebra or more generally of an A-infinity algebra with certain constructions of Chen and Gugenheim. Thereafter we…

We study constructive $A_\infty$-models of the DG-category of matrix factorisations of a potential over a commutative $\mathbb{Q}$-algebra $k$, consisting of a Hom-finite $A_\infty$-category equipped with an $A_\infty$-idempotent functor.

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…

Using the theory infinity-categories we construct derived (dg-)categories of regular, holonomic D-modules and algebraically constructible sheaves on a complex smooth algebraic stack. We construct a natural infinity-categorical equivalence…

The class of quantum affinizations includes quantum affine algebras and quantum toroidal algebras. In general they have no Hopf algebra structure, but have a "coproduct" (the Drinfeld coproduct) which does not produce tensor products of…

We show for an affine variety $X$, the derived category of quasi-coherent $D$-modules is equivalent to the category of DG modules over an explicit DG algebra, whose zeroth cohomology is the ring of Grothendieck differential operators…

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…

The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…

We propose a solution to the "curvature problem" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let $k$ be a field, $A$ a dg algebra over $k$ and $A_n = A[t]/(t^{n+1})$ a cdg algebra over $R_n = k[t]/(t^{n+1})$,…

Given an additive category $\mathcal{C}$ and an integer $n\geqslant 2$. We form a new additive category $\mathcal{C}[\epsilon]^n$ consisting of objects $X$ in $\mathcal{C}$ equipped with an endomorphism $\epsilon_X$ satisfying…