Related papers: On exact dg categories
Let $\mathcal{X}$ be a resolving and contravariantly finite subcategory of $\rm{mod}\mbox{-}\Lambda$, the category of finitely generated right $\Lambda$-modules. We associate to $\mathcal{X}$ the subcategory…
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…
We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-). In an intermediate step, we prove…
We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical nerves. It is shown that every necklicial nerve can be…
We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated…
The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent sheaves, for the triangulated categories of…
In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to…
This paper establishes the homological and geometric foundations of non-commutative n-ary Gamma-semirings, unifying two previously distinct directions in Gamma-algebra: the derived Gamma-geometry developed for the commutative ternary case…
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…
This paper examines the concept of a stratified exact category in the context of number rings and corresponding Galois groups. BGG reciprocity and duality are proven for these categories making them highest weight categories. The strong…
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…
We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring $\mathbb{F}_p[G]$ of an elementary abelian $p$-group $G$ in terms of commutative algebra. This extends results of Carlsson…
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…
Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of mutation of subcategories in an extriangulated category is defined in this…
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…
We introduce the notions of normal tensor functor and exact sequence of tensor categories. We show that exact sequences of tensor categories generalize strictly exact sequences of Hopf algebras as defined by Schneider, and in particular,…
We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties…
We introduce and study several homological notions which generalise the discrete derived categories of D. Vossieck. As an application, we show that Vossieck discrete algebras have this property with respect to all bounded t-structures. We…
Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category $\mathcal{E}$ is a cotilting torsionfree class of an abelian category. In fact, this property characterizes…
We introduce a notion of exact quasicategory, and we prove an analogue of Amnon Neeman's Theorem of the Heart for Waldhausen K-theory.