Equivariant Morita theory for graded tensor categories
نویسندگان
چکیده
We extend categorical Morita equivalence to finite tensor categories gra\-ded by a group $G$. show that two such are graded equivalent if and only their equivariant Drinfeld centers as braided $G$-crossed categories.
منابع مشابه
Morita Theory for Finitary 2-categories
We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.
متن کاملOn Equivariant Homotopy Theory for Model Categories
Two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category are studied and compared. For the topological model category of spaces, we recover that the categories of topological presheaves indexed by the orbit category of a fixed topological group G and the category of G-spaces form Quillen equivalent model categories.
متن کاملClifford theory for tensor categories
A graded tensor category over a group G will be called a strongly G-graded tensor category if every homogeneous component has at least one invertible object. Our main result is a description of the module categories over a strongly G-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of G.
متن کاملMorita classes of algebras in modular tensor categories
We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two simple algebras with non-degenerate trace pairing are Morita-equivalent if and only if their full centres are isomorphic as algebras. This result has an int...
متن کاملMorita Theory for Derived Categories: a Bicategorical Perspective
We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita theory in derived and bicategorical contexts. This is motivated by study of Rickard’s theorem for derived equivalences of rings and of Morita theory for ring ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Simon Stevin
سال: 2022
ISSN: ['1370-1444', '2034-1970']
DOI: https://doi.org/10.36045/j.bbms.210720