Free algebras and automata realizations in the language of categories
From triangulated categories to cluster algebras II
Functional separation of inductive limits and representation of presheaves by sections. Part II. Embedding of presheaves into presheaves of compact spaces
Functors on locally finitely presented additive categories
-quasi-Frobenius Lie algebras
A Lie version of Turaev’s -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a -quasi-Frobenius Lie algebra for a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra together with a left -module structure which acts on via derivations and for which is -invariant. Geometrically, -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...
Gabriel filters in Grothendieck categories.
In [1] it is proved that one must take care trying to copy results from the case of modules to an arbitrary Grothendieck category in order to describe a hereditary torsion theory in terms of filters of a generator. By the other side, we usually have for a Grothendick category an infinite family of generators {Gi; i ∈ I} and, although each Gi has good properties the generator G = ⊕i ∈ I Gi is not easy to handle (for instance in categories like graded modules). In this paper the authors obtain a bijective...
GAGA for DQ-algebroids
Galois coverings, Morita equivalence and smash extensions of categories over a field.
Ganea term for CCG-homology of crossed modules.
In [2] an internal homology theory of crossed modules was defined (CCG-homology for short), which is very much related to the homology of the classifying spaces of crossed modules ([5]). The goal of this note is to construct a low-dimensional homology exact sequence corresponding to a central extension of crossed modules, which is quite similar to the one constructed in [3] for group homology.
Generalized Brown representability in homotopy categories.
Generalized flatness and coherence
Generalized injectivity
Generalized projectivity
Generalized projectivity. II.
Generation of preradicals
Gorenstein dimension of abelian categories arising from cluster tilting subcategories
Let be a triangulated category and be a cluster tilting subcategory of . Koenig and Zhu showed that the quotient category is Gorenstein of Gorenstein dimension at most one. But this is not always true when becomes an exact category. The notion of an extriangulated category was introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. Now let be an extriangulated category with enough projectives and enough injectives, and a cluster...
Gorenstein star modules and Gorenstein tilting modules
We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between -Gorenstein star modules and -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of -Gorenstein tilting modules.
Graded blocks of group algebras with dihedral defect groups
We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.
Graphes sans circuit et bilinéarité
Hall algebras of two equivalent extriangulated categories
For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a by-product,...