## 49 Citations

Covering theory, (mono)morphism categories and stable Auslander algebras

- Mathematics
- 2020

Let $\mathcal{A}$ be a locally bounded $k$-category and $G$ a torsion-free group of $k$-linear automorphisms of $\mathcal{A}$ acting freely on the objects of $\mathcal{A},$ and…

On Frobenius (completed) orbit categories

- Mathematics
- 2015

Let ${\mathcal E}$ be a Frobenius category, ${\mathcal P}$ its subcategory of projective objects and $F:{\mathcal E} \to {\mathcal E}$ an exact automorphism. We prove that there is a fully faithful…

On Standard Derived Equivalences of Orbit Categories

- Mathematics
- 2015

Let k be a commutative ring, A$\mathcal {A}$ and ℬ$\mathcal {B}$ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ$\mathcal…

Singularity categories of locally bounded categories with radical square zero

- Mathematics
- 2019

This paper studies several singularity categories of a locally bounded $k-$linear category $\mathscr{C}$ with radical square zero. Following the work of Bautista and Liu [6], we give a complete…

Singularity categories of representations of quivers over local rings.

- Mathematics
- 2017

Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathbb{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the…

Gorenstein modifications and \mathds{𝑄}-Gorenstein rings

- Mathematics
- 2016

Let $R$ be a Cohen--Macaulay normal domain with a canonical module $\omega_R$. It is proved that if $R$ admits a noncommutative crepant resolution (NCCR), then necessarily it is…

Derived Equivalences of Actions of a Category

- MathematicsAppl. Categorical Struct.
- 2013

This work investigates derived equivalences of those oplax functors, and establishes a Morita type theorem for them, which gives a base of investigations of derived equivalence of Grothendieck constructions of those Oplaxfunctors.

On a family of Caldero–Chapoton algebras that have the Laurent phenomenon

- MathematicsJournal of Algebra
- 2019

## References

SHOWING 1-10 OF 28 REFERENCES

Skew category, Galois covering and smash product of a k-category

- Mathematics
- 2003

In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew…

Graphs with relations, coverings and group-graded algebras

- Mathematics
- 1983

The paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs. To include gradings of all basic…

Group-graded rings and duality

- Mathematics
- 1985

We give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by Cohen and Montgomery in [1]. This duality is then used to extend known…

On triangulated orbit categories

- Mathematics
- 2005

We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by A. Buan, R.…

Deriving DG categories

- Mathematics
- 1994

— We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5],…

Galois coverings, Morita equivalence and smash extensions of categories over a field.

- Mathematics
- 2005

Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a…