Related papers: On the structure of modules indexed by small categ…

A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…

Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show…

For any ring $A$ and a small, preadditive, Hom-finite, and locally bounded category $Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors from $Q$ to the category of…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class CogenM is always a covering class whenever M is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given. As…

From a bimodule $M$ over an exact category $C$, we define an exact category $C\ltimes M$ with a projection down to $C$. This construction classifies certain split square zero extensions of exact categories. We show that the trace map…

A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this note, Mitchell's embedding theorem for a tame schemoid is established. The result allows us to give a cofibrantly generated model…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

Let (A,m_A) -> (B,m_B) be a local morphism of local noetherian rings and M a finitely generated B-module. Then it follows from Tor^A_1(M,A/m_A) = 0 that M is a flat A-module. This is usually called the "local criterion of flatness". We give…

To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…

In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual…

This paper proves that the functor $C(*)$ that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type --- even inducing an…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

In this paper, we associate a new topology to a nonzero unital module $M$ over a commutative $R$, which is called Golomb topology of the $R$-module $M$. Let $M\ $be an\ $R$-module and $B_{M}$ be the family of coprime cosets $\{m+N\}$ where…

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ and a left adjoint symmetric monoidal fiber functor to $\operatorname{Mod}_A^{\otimes}$ for some $\mathbb{E}_{\infty}$-ring $A$, one can construct a derived group scheme $G$…

This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are…

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…

Let $(R,\frak m)$ be a commutative noetherian local ring. In this paper, we prove that if $\frak m$ is decomposable, then for any finitely generated $R$-module $M$ of infinite projective dimension $\frak m$ is a direct summand of (a direct…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

We study quasidiagonality and local reflexivity for $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. We introduce and study a notion of amenability for vector valued traces.