Related papers: Comparison of Abelian categories recollements

In this paper, we construct derived equivalences between two subrings of relevant $\Phi$-Auslander-Yoneda rings from an arbitrary short exact sequence in an abelian category. As a consequence, any short exact sequence in an abelian category…

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework.…

In this paper, we state the notion of morphisms in the category of abelian crossed modules and prove that this category is equivalent to the category of strict Picard categories and regular symmetric monoidal functors. The theory of…

This is mostly an overview. Given finitely presentable abelian categories $A$ and $B$, we sketch the construction of an abelian category of continuous functors from $A$ to $B$ that has nice $2$-categorical behaviour and gives an explicit…

We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…

A recollement of triangulated categories describes one such category as being "glued together" from two others. This paper gives a precise criterion for the existence of a recollement of the derived category of a Differential Graded Algebra…

nspired by the work of J$\o$rgensen [J], we define a (upper-, lower-) symmetric recollements; and give a one-one correspondence between the equivalent classes of the upper-symmetric recollements and one of the lower-symmetric recollements,…

We fix any bicategory $\mathscr{A}$ together with a class of morphisms $\mathbf{W}_{\mathscr{A}}$, such that there is a bicategory of fractions $\mathscr{A}[\mathbf{W}_{\mathscr{A}}^{-1}]$. Given another such pair…

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…

In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…

We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simple algebras which are…

The purpose of this short and elementary note is to identify some classes of exact categories introduced in L. Previdi's thesis. Among other things we show: (1) An exact category is partially abelian exact if and only if it is abelian. (2)…

We consider a class of homogeneous self-similar sets with complete overlaps and give a sufficient condition for the Lipschitz equivalence between members in this class.

In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements…

We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.

This Bachelor's thesis studies Adelman's construction of the universal abelian category of an additive category. It furthermore extends the construction such that it also applies to transformations between additive functors.

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…

In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by…

We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…