Related papers: Extriangulated factorization systems, $s$-torsion …

We study the number of ways of factoring elements in the complex reflection groups G(r,s,n) as products of reflections. We prove a result that compares factorization numbers in G(r,s,n) to those in the symmetric group on n letters, and we…

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. In this paper, we study Gorenstein derived functors for extriangulated categories. More precisely, we first…

We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…

Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a…

In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of…

It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is semi-abelian. In this article, we consider a special kind of hearts of twin cotorsion pairs induced by $d$-cluster tilting subcategories in…

Hovey's correspondence between model structures and cotorsion pairs in the setting of abelian categories, has been generalized by Nakaoka-Palu, using two cotorsion pairs, to the setting of weakly idempotent complete extriangulated…

Every Grothendieck fibration gives rise to a vertical/cartesian orthogonal factorization system on its domain. We define a cartesian factorization system to be an orthogonal factorization in which the left class satisfies 2-of-3 and is…

The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories…

We associate a complete intersection singularity to a graded matrix factorization of size two of a polynomial in three variables. We show that we get an inverse to the reduction of singularities considered by C.T.C.Wall. We study this for…

In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…

We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads…

We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…

We give a complete classification of (co)torsion pairs in finite $2$-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting. These finite $2$-Calabi-Yau triangulated categories are divided into two main…

In this paper we extend several classical results on pointed torsion theories -- also known as torsion pairs -- to the setting of non-pointed torsion theories defined via kernels and cokernels relative to a fixed class of trivial objects…

We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…

This paper examines a systematic method to construct a pair of (inter-related) root systems for arbitrary Coxeter groups from a class of non-standard geometric representations. This method can be employed to construct generalizations of…

These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to…

We introduce signed exceptional sequences as factorizations of morphisms in the cluster morphism category. The objects of this category are wide subcategories of the module category of a hereditary algebra. A morphism $[T]:\mathcal A\to…

We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathfrak{t}$ on a stable $\infty$-category $\mathbf{C}$ is equivalent to a normal…