We show that the quotients of the continuous cluster category Cπ and the rational subcategory X modulo the additive subcategory generated by any cluster are abelian categories and we show that they are isomorphic to categories of infinite and finite length modules, respectively, over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-ChapotonSchiffler and Buan-M...

Let R be a commutative ring whose complete ring of quotients is Rinjective. We show that the category of topological R-modules contains a full subcategory that is ∗-autonomous using R itself as dualizing object. In order to do this, we develop a new variation on the category chu(D, R), where D is the category of discrete R-modules: the high wide subcategory, which we show equivalent to the cate...

Let G be a finite group and let k be a field whose characteristic p divides the order of G. Freyd’s generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if G has periodic cohomology then the gen...

It is well known that the category MC of right comodules over an A-coring C, A an associative ring, is a subcategory of the category of left modules ∗CM over the dual ring ∗C. The main purpose of this note is to show that MC is a full subcatgeory in ∗CM if and only if C is locally projective as a left A-module.

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

We study localizing and colocalizing subcategories of a comodule category of a coalgebra C over a field, using the correspondence between localizing subcategories and equivalence classes of idempotent elements in the dual algebra C∗. In this framework, we give a useful description of the localization functor by means of the Morita–Takeuchi context defined by the quasi-finite injective cogenerat...

Let R be a commutative Noetherian Henselian local ring. Denote by modR the category of finitely generated R-modules, and by G the full subcategory of modR consisting of all G-projective R-modules. In this paper, we consider when a given R-module has a right G-approximation. For this, we study the full subcategory rapG of modR consisting of all R-modules that admit right G-approximations. We inv...

Abstract Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors ${\operatorname{mod}}$-$\mathcal{M}$ modulo subcategory effaceable ${\operatorname{mod}}_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory, which is equivalent to $\mathcal{M}$. This gives higher-dimensional version Auslander’s formula.