Related papers: Spectral sequences via linear presheaves
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of…
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of $20$ topics in spectral graph theory,…
We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness…
In this paper we study the homotopy theory of parameterized spectrum objects in the $\infty$-category of $(\infty, 2)$-categories, as well as the Quillen cohomology of an $(\infty, 2)$-category with coefficients in such a parameterized…
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…
For any finite group G, we construct a spectral sequence for computing the Bredon cohomology of a G-CW complex X, starting with the cohomology of X^H/\cup_{K>H}X^K with suitable local coefficients, for various H \leq G.
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
In this paper we present the notion of smooth CW complexes given by attaching cubes on the category of diffeological spaces, and we study their smooth homotopy structures related to the homotopy extension property.
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
We develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct…
We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…
We introduce the concept of an infinite cochain sequence and initiate a theory of homological algebra for them. We show how these sequences simplify and improve the construction of infinite coclass families (as introduced by Eick and…
We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes…
In this work, we construct a persistent version of the well-known Leray spectral sequence. More precisely, we construct a spectral sequence that computes the persistent cohomology of a space from the persistent cohomology in each open set…
A stable model category is a setting for homotopy theory where the suspension functor is invertible. The prototypical examples are the category of spectra in the sense of stable homotopy theory and the category of unbounded chain complexes…
As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…
The sequence space of all real-valued sequences, denoted $Seq(\mathbb{R})$, is typically investigated through the lens of infinite-dimensional vector spaces, utilizing Banach space norms or Schauder bases. This work proposes a…
The James fibrations give rise to the geometric EHP sequences of homotopy groups of spheres. Using techniques from the Lambda algebra, \cite{BCKQRS66} shows that there are similar long exact sequences of Ext groups defining the $E_{2}-$page…
We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…