Related papers: Perfect category-graded algebras

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties,…

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

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…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

We explain how categories, and groupoids, can be seen as models for a Lawvere ${\mathfrak Gr}$-theory, where ${\mathfrak Gr}$ is the category of graphs, and show that for Lawvere ${\mathfrak Gr}$-theories finitely presentable models are…

Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…

In this note, we propose a generalisation of G. Janelidze's notion of an ideally exact category beyond the Barr exact setting. We define an ideally regular category as a regular, Bourn protomodular category with finite coproducts in which…

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that the elementary subgroup E(R) of group of points G(R) is correctly defined. Then E(R) is perfect, except for the well-known cases of a split reductive…

We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a…

We compute the Krull-Gabriel dimension of the category of perfect complexes for finite dimensional algebras which are derived discrete.

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…

We introduce the notion of a "category with path objects", as a slight strengthening of Kenneth Brown's classic notion of a "category of fibrant objects". We develop the basic properties of such a category and its associated homotopy…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of group schemes and are in correspondence with graded Hopf algebra. In this setting, graded group varieties…

It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted…

Perfect ideals $I$ of grade $3$ in a local ring $(R,\mathfrak{m},\Bbbk)$ can be classified based on multiplicative structures on $\text{Tor}^R_{\bullet}(R/I,\Bbbk)$. The classification is incomplete in the sense that it remains open which…

Let O be a topological (colored) operad. The Lurie infinity-category of O-algebras with values in (infinity-category of) complexes is compared to the infinity-category underlying the model category of (classical) dg O-algebras. This can be…

We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type E6. For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit…

We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its…