English
Related papers

Related papers: Morita equivalence methods in classification of fu…

200 papers

We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo…

Quantum Algebra · Mathematics 2011-09-08 Alexei Davydov , Michael Mueger , Dmitri Nikshych , Victor Ostrik

With a rapidly increasing amount and diversity of remote sensing (RS) data sources, there is a strong need for multi-view learning modeling. This is a complex task when considering the differences in resolution, magnitude, and noise of RS…

Computer Vision and Pattern Recognition · Computer Science 2023-10-24 Francisco Mena , Diego Arenas , Marlon Nuske , Andreas Dengel

We prove a group graded Morita equivalences version of the "butterfly theorem" on character triples. This gives a method to construct an equivalence between block extensions from another related equivalence.

Representation Theory · Mathematics 2023-04-26 Andrei Marcus , Virgilius-Aurelian Minuta

We establish a Morita theorem to construct triangle equivalences between the singularity categories of (commutative and non-commutative) Gorenstein rings and the cluster categories of finite dimensional algebras over fields, and more…

Representation Theory · Mathematics 2024-10-15 Norihiro Hanihara , Osamu Iyama

We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister's theory of the local structure of…

Rings and Algebras · Mathematics 2010-03-30 Mark V. Lawson

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

Group Theory · Mathematics 2010-04-02 Ganna Kudryavtseva , Volodymyr Mazorchuk

In this paper, we propose a new approach towards the classification of spherical fusion categories by their Frobenius-Schur exponents. We classify spherical fusion categories of Frobenius-Schur exponent 2 up to monoidal equivalence. We also…

Quantum Algebra · Mathematics 2020-11-30 Zheyan Wan , Yilong Wang

We define the Drinfeld center of a monoidal category enriched over a braided monoidal category, and show that every modular tensor category can be realized in a canonical way as the Drinfeld center of a self-enriched monoidal category. We…

Category Theory · Mathematics 2020-06-05 Liang Kong , Hao Zheng

Monads are well known to be equivalent to lax functors out of the terminal category. Morita contexts are here shown to be lax functors out of the chaotic category with two objects. This allows various aspects in the theory of Morita…

Category Theory · Mathematics 2014-05-21 Stephen Lack

The main purpose of this paper is to introduce a new category, which we call a resonance category, whose combinatorics reflect that of canonical stratifications of $n$-fold symmetric smash products. The study of the stratifications can then…

Category Theory · Mathematics 2007-05-23 Dmitry N. Kozlov

We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product. We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion…

Quantum Algebra · Mathematics 2021-05-28 Thomas A. Wasserman

For a fusion category, we prove some new integral properties concerning the dimension of a simple object that generates a Isaacs fusion subcategory. A stronger divisibility result is proven for any modular fusion category. This divisibility…

Quantum Algebra · Mathematics 2025-07-11 S. Burciu

We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category ${\mathcal C}$ to be equivalent. This concludes the classification of such module…

Quantum Algebra · Mathematics 2017-06-20 Sonia Natale

We prove that if two associative deformations (parameterized by the same complete local ring) are derived Morita equivalent, then they are Morita equivalent (in the classical sense).

Rings and Algebras · Mathematics 2009-07-14 Amnon Yekutieli

We describe the origins of the theory of tannakian categories, and summarize its main results.

Algebraic Geometry · Mathematics 2025-02-25 James S Milne

This paper is devoted to the study of Morita equivalence for twisted Poisson manifolds. We review some Morita invariants and prove that integrable twisted Poisson manifolds which are gauge equivalent are Morita equivalent. Moreover, we…

Symplectic Geometry · Mathematics 2015-03-17 Yuji Hirota

We consider traces on module categories over pivotal fusion categories which are compatible with the module structure. It is shown that such module traces characterise the Morita classes of special haploid symmetric Frobenius algebras.…

Quantum Algebra · Mathematics 2018-05-09 Gregor Schaumann

We prove a version of the Jordan-H\" older theorem in the context of weakly group-theoretical fusion categories. This allows us to introduce the composition factors and the length of such a fusion category C, which are in fact Morita…

Quantum Algebra · Mathematics 2015-12-15 Sonia Natale

We establish rank-finiteness for the class of $G$-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly…

Quantum Algebra · Mathematics 2019-02-19 Corey Jones , Scott Morrison , Dmitri Nikshych , Eric C. Rowell

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…

Category Theory · Mathematics 2016-01-06 Randall D. Helmstutler