Related papers: A note on Closure Operators in Category of Modules

Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

We show, for a smooth projective variety $X$ over an algebraically closed field $k$ with an effective Cartier divisor $D$, that the torsion subgroup $\CH_0(X|D)\{l\}$ can be described in terms of a relative {\'e}tale cohomology for any…

The study of modules over a finite von Neumann algebra ${\mathcal A}$ can be advanced by the use of torsion theories. In this work, some torsion theories for ${\mathcal A}$ are presented, compared and studied. In particular, we prove that…

We study classes of modules closed under direct sums, $\mathcal{M}$-submodules and $\mathcal{M}$-epimorphic images where $\mathcal{M}$ is either the class of embeddings, $RD$-embeddings or pure embeddings. We show that the…

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

Let R be a commutative Noetherian domain, and let M and N be finitely generated R-modules. We give new criteria for determining when M tensor N has torsion. We also give constructive formulas for producing a module in the isomorphism class…

We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting module. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

In the category $\mathcal{P}_{d}$ of strict polynomial functors, the morphisms between extension groups induced by the Frobenius twist are injective. In \cite{Cuo14a}, the category $\mathcal{P}_{d}$ is proved to be a full sub-category of…

We extend the classification results for torsion classes and torsion-free classes in the category of finitely generated modules over a commutative noetherian ring to suitable symmetric monoidal closed noetherian abelian categories. Our main…

An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are…

We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this operator. A key finding is the decisive nature of this…

In this article, we prove that induced modules of support $\tau$-tilting modules over blocks of finite groups satisfying inertial-invariant condition are also support $\tau$-tilting modules.

We describe how some aspects of abstract localization on module categories have applications to the study of injective comodules over some special types of corings. We specialize the general results to the case of Doi-Koppinen modules,…

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to…

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking…

We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial…

We study two subcategories of the category of artinian modules, a wide subcategory and a Serre subcategory. We prove that all wide subcategories of artinian modules are Serre subcategories. We also provide the bijection between the set of…

We develop further the theory of operads and analytic functors. In particular, we introduce a bicategory that has operads as 0-cells, operad bimodules as 1-cells and operad bimodule maps as 2-cells, and prove that this bicategory is…