Related papers: Derived categories of bifiltered complexes

We construct a Kawamata type semiorthogondal decomposition for the bounded derived category of coherent sheaves of nodal quintic del Pezzo threefolds, decomposing the bounded derived category into bounded derived categories of finite…

We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…

We describe some of the basic properties of the 2-category of 2-term complexes in an abelian category, using butterflies as morphisms.

We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…

We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

We instal homological algebra, including derived functors, on certain non-additive categories like categories of pointed CW-complexes, modules of monoids or sheaves thereof. We apply this theory to Monoid schemes and sheaves on them,…

Let $I$ be an arbitrary ideal generated by binomials. We show that certain equivalence classes of fibers are associated to any minimal binomial generating set of $I$. We provide a simple and efficient algorithm to compute the indispensable…

A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

We develop structure theory of finite Lie conformal superalgebras.

We define the derived category of quasi--coherent modules for certain Artin stacks as the homotopy category of two Quillen monoidal model structures on the corresponding category of unbounded complexes of quasi--coherent modules.

Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-categories over a finite semisimple tensor 1-category. Then,…

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…

We invent the notion of a derived and fluid variety. Fluid variety has no proper derived variety as its subvariety. We examine some properties of fluid and derived varieties. Examples of such varieties of bands are presented.

We construct a stable infinity category with objects flow categories and morphisms flow bimodules; our construction has many flavors, related to a choice of bordism theory, and we discuss in particular framed bordism and the bordism theory…