Related papers: Reflexive modules and Auslander-type conditions

This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian category,…

The representations of a quiver Q over a field k have been studied for a long time. It seems to be worthwhile to consider also representations of Q over arbitrary finite-dimensional k-algebras A. Here we draw the attention to the case when…

A semi-localization of a category is a full reflective subcategory with the property that the reflector is semi-left-exact. In this article we first determine an abstract characterization of the categories which are semi-localizations of an…

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

Two unital operator algebras A, B are called Delta-equivalent if there exists an equivalence functor between the categories A-mod and B-mod which "extends" to a *-functor implementing an equivalence between the categories A-dmod and B-dmod.…

Let $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for…

Let $\text{Gprj}\mbox{-}\Lambda$ denote the category of Gorenstein projective modules over an Artin algebra $\Lambda$ and the category $\text{mod}\mbox{-} (\underline{\text{Gprj}}\mbox{-}\Lambda)$ of finitely presented functors over the…

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ of admissibly finitely presented functors and use it to give a version…

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In…

A ring R satisfies the Generalized Auslander-Reiten Condition if any R-module M with no self-extensions in degrees higher than m must have projective dimension at most m. We prove that this condition is satisfied by all n-symmetric algebras…

We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…

We consider the quantum affine vertex algebra $\mathcal{V}_{c}(\mathfrak{gl}_N)$ associated with the rational $R$-matrix, as defined by Etingof and Kazhdan. We introduce certain subalgebras $\textrm{A}_c (\mathfrak{gl}_N)$ of the completed…

We give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose Auslander-Reiten quiver admits a generalized standard family of quasi-tubes maximally saturated by simple and projective…

In this paper we prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-filtered colimits is a…

We characterize projective objects in the category of internal crossed modules within any semi-abelian category. When this category forms a variety of algebras, the internal crossed modules again constitute a semi-abelian variety, ensuring…

The category of abelian varieties over $\mathbb{F}_q$ is shown to be anti-equivalent to a category of $\mathbb{Z}$-lattices that are modules for a non-commutative pro-ring of endomorphisms of a suitably chosen direct system of abelian…

We prove that the category 2-$ \mathrm{Grpd}(\mathscr{C}) $ of internal $2$-groupoids is a Birkhoff subcategory of the category $ \mathrm{Grpd}^2(\mathscr{C}) $ of double groupoids in a regular Mal'tsev category $\mathscr{C}$ with finite…

We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda…

A quasi-Hopf algebra $H$ can be seen as a commutative algebra $A$ in the centre $\mathcal Z(H-Mod)$ of $H-Mod$. We show that the category of $A$-modules in $\mathcal Z(H-Mod)$ is equivalent (as a monoidal category) to $H-Mod$. This can be…

We study Mittag-Leffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting…