相关论文: Relative Commutator Theory in Semi-Abelian Categor…

We investigate relative cohomology functors on subcategories of abelian categories via Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that certain comparison maps between these functors are isomorphisms…

In this paper we introduce a special kind of relative (co)resolutions associated to a pair of classes of objects in an abelian category $\mathcal{C}.$ We will see that, by studying these relative (co)resolutions, we get a possible…

A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets…

In this paper, we establish the global analogues of some dualities and equivalences in local algebra by developing the theory of relative Cohen-Macaulay modules. Let R be a commutative Noetherian ring (not necessarily local) with identity…

The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality…

The goal of this thesis is to define a 2-dimensional version of abelian categories, where symmetric 2-groups play the role that abelian groups played in 1-dimensional algebra. Abelian and 2-abelian groupoid enriched categories are defined…

By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once…

To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we…

This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them. A simple definition of an abelian categorification is presented and illustrated with…

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…

In a previous paper we showed that the category of cocommutative color Hopf algebras is semi-abelian in case the group $G$ is abelian and finitely generated and the characteristic of the base field is different from 2 (not needed if $G$ is…

Higher homological algebra, basically done in the framework of an $n$-cluster tilting subcategory $\mathcal{M}$ of an abelian category $\mathcal{A}$, has been the topic of several recent researches. In this paper, we study a relative…

In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…

Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with $\mu_n \subset K$, and choose $\omega \in \mu_n$ a primitive $n$th root of unity. Denote the absolute Galois group of $K$ by $\operatorname{Gal}(K)$, and the…

We describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We…

The adjunction between coalgebras and Hopf algebras, first described by Takeuchi, allows one to prove that the semi-abelian category of cocommutative Hopf algebras has enough $\mathcal E$-projective objects with respect to the class…

We construct equivalences among four notions associated to a reductive group scheme $G$: factorization super central extensions of the loop group of $G$ by $\mathbb G_m$ subject to a condition on the commutator, factorization super line…

The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated…

We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a…

An abelian self-commutator in a C*-algebra $\mathcal{A}$ is an element $A$ that can be written as $A=X^*X-XX^*$, with $X\in\mathcal{A}$ such that $X^*X$ and $XX^*$ commute. It is shown that, given a finite AW*-factor $\mathcal{A}$, there…