Related papers: A note on singular equivalences and idempotents

We study the notion of \emph{separable algebras} in the context of symmetric monoidal stable $\infty$-categories. In the first part of this paper, we compare this context to that of tensor-triangulated categories and show that separable…

We introduce the notion of $\mathbb{E}_\infty$-descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are $\mathbb{E}_\infty$-descendable. As an application, we prove a variant of…

In this paper we show that the (un)bounded derived categories$\colon$(i) of the monomorphism category, (ii) of the morphism category and (iii) of the double morphism category, admit a periodic infinite ladder of recollements. These results…

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…

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between…

Stable equivalences of Morita type preserve many interesting properties and is proved to be the appropriate concept to study for equivalences between stable categories. Recently the singularity category attained much attraction and Xiao-Wu…

Let $\Lambda$ be an artin algebra and let $\mathcal{P}^{<\infty}_\Lambda$ the category of finitely generated right $\Lambda$-modules of finite projective dimension. We show that $\mathcal{P}^{<\infty}_\Lambda$ is contravariantly finite in…

In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…

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 define the notion of a $\lambda$-definable category, a generalisation of the notion of definable category from the model theory of modules. Let ${\cal C}$ be a $\lambda$-accessible additive category. We characterise the additive functors…

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb{R}$ or $\mathbb{C}$. We prove an adelic version of…

Let $k$ be an algebraically closed field and $A$ be a (left and right) Noetherian associative $k$-algebra. Assume further that $A$ is either positively graded or semiperfect (this includes the class of finite dimensional $k$-algebras, and…

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…

We find two series expansions for Legendre's second incomplete elliptic integral $E(\lambda, k)$ in terms of recursively computed elementary functions. Both expansions converge at every point of the unit square in the $(\lambda, k)$ plane.…

For a finite-dimensional algebra {\Lambda}, we establish an explicit bijection between widely generated torsion(-free) classes and semibricks in mod {\Lambda}. Using the kappa order on the lattice of torsion classes with canonical join…

We establish the $\#P$-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing $\lambda$-immanants of $0$-$1$ matrices is $\#P$-hard whenever the…

We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…

The purpose of this note is to resolve a conjecture in arXiv:2307.00442(4), regarding the initial algebra for the enrichment endofunctor $(-)\mathbf{Cat}$ over general symmetric monoidal $(\infty, 1)$-categories. We prove that Ad\'amek's…

The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…