Related papers: Highest weight categories and recollements
Recently left Schur subcategories in a length abelian category were introduced by Enomoto, which unify torsion-free classes and wide subcategories. In this paper, we show the construction of left Schur subcategories in the recollements of…
In this survey we discuss some combinatorial aspects of higher cluster categories.
Surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories. These `stratifying' recollements are derived from recollements of module categories. Can every recollement be…
In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on…
Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement $(\mathcal A ,\mathcal…
This article deals with a relationship between derived categories of modules over some partially ordered sets and triangulated categories arising from quasi-homogeneous isolated singularities. It produces heuristics for the existence of…
We study the concept of hypervaluations on hyperfields. In particular, we show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of a hypervaluation onto an ordered abelian group (which…
Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
Given an abelian category, we characterize the long exact sequences of length six which can be obtained from the snake lemma. Equivalently, these are the long exact sequences which arise as the homology of a triangle in the corresponding…
We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer-Thrall Conjecture for artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey.
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…
In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
We introduce and investigate (dual) relative split objects with respect to a fully invariant short exact sequence in abelian categories. We compare them with (dual) relative Rickart objects, and we study their behaviour with respect to…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories by aggregating the individual classifications, and no category can be left empty. An aggregator satisfies \emph{Expertise} if individuals are…
We study a category of modules over $\mathfrak{gl}(\infty)$ analogous to category $\mathcal O$. We fix adequate Cartan, Borel and Levi-type subalgebras $\mathfrak h, \mathfrak b$ and $\mathfrak l$ with $\mathfrak l \cong…
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…