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45,751
The 3category of tensor categories
, 2014
"... Abstract. We investigate the relationship between the algebra of tensor categories and the topology of framed 3manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3dualizab ..."
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Cited by 4 (2 self)
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Abstract. We investigate the relationship between the algebra of tensor categories and the topology of framed 3manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3
CLIFFORD THEORY FOR TENSOR CATEGORIES
, 2009
"... A graded tensor category over a group G will be called a strongly Ggraded 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 Ggraded tensor category as induced from module categories over tens ..."
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Cited by 10 (4 self)
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A graded tensor category over a group G will be called a strongly Ggraded 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 Ggraded tensor category as induced from module categories over
Monads on Tensor Categories
 J. Pure Appl. Algebra
, 2002
"... this paper we will discuss the combination of two classical notions of category theory, both treated extensively in [CWM]. One of these is the notion of a monad or triple on a category, which goes back to Godement [G] and was rst developed by Eilenberg, Moore, Beck and others. The other is that of a ..."
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Cited by 49 (1 self)
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is that of a monoidal category or tensor category, which originates with Benabou [Be] and with Mac Lane's famous coherence theorem [MacL], and which pervades much of present day mathematics. For a monad S on a tensor category, there is a natural additional structure that one can impose, namely that of a
Finite tensor categories
 Moscow Math. Journal
"... These are lecture notes for the course 18.769 “Tensor categories”, taught by P. Etingof at MIT in the spring of 2009. In these notes we will assume that the reader is familiar with the basic theory of categories and functors; a detailed discussion of this theory can be found in the book [ML]. We wil ..."
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Cited by 75 (12 self)
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These are lecture notes for the course 18.769 “Tensor categories”, taught by P. Etingof at MIT in the spring of 2009. In these notes we will assume that the reader is familiar with the basic theory of categories and functors; a detailed discussion of this theory can be found in the book [ML]. We
On exotic modular tensor categories
 Commun. Contemp. Math
"... Abstract. We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular Smatrix S and −S has both topological and physical significance, so in our convention there are a tot ..."
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Cited by 37 (12 self)
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Abstract. We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular Smatrix S and −S has both topological and physical significance, so in our convention there are a
C∗ALGEBRAS IN TENSOR CATEGORIES
, 2007
"... We define and systematically study nonassociative C∗algebras as C∗algebras internal to a topological tensor category. We also offer a concrete approach to these C∗algebras, as Ginvariant, norm closed ∗subalgebras of bounded operators on a GHilbert space, with deformed composition product. Our ..."
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Cited by 2 (2 self)
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We define and systematically study nonassociative C∗algebras as C∗algebras internal to a topological tensor category. We also offer a concrete approach to these C∗algebras, as Ginvariant, norm closed ∗subalgebras of bounded operators on a GHilbert space, with deformed composition product. Our
TANNAKA DUALS IN SEMISIMPLE TENSOR CATEGORIES
, 2001
"... Abstract. Tannaka duals of Hopf algebras inside semisimple tensor categories are used to construct orbifold tensor categories, which are shown to include the Tannaka dual of the dual Hopf algebras. The second orbifolds are then canonically isomorphic to the initial tensor categories. ..."
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Cited by 4 (0 self)
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Abstract. Tannaka duals of Hopf algebras inside semisimple tensor categories are used to construct orbifold tensor categories, which are shown to include the Tannaka dual of the dual Hopf algebras. The second orbifolds are then canonically isomorphic to the initial tensor categories.
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The comp ..."
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Cited by 37 (12 self)
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We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations
On Vafa’s theorem for tensor categories
 MR MR1906068 (2003i:18009) SIUHUNG NG AND PETER SCHAUENBURG
"... In this note we prove two main results. 1. In a rigid braided finite tensor category over C (not necessarily semisimple), ..."
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Cited by 11 (2 self)
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In this note we prove two main results. 1. In a rigid braided finite tensor category over C (not necessarily semisimple),
Algebras and their dual in rigid tensor categories
 Int. Math. Forum
"... It is known that if H is an algebra (resp. a coalgebra) in a rigid tensor category, then its dual H ∗ is a coalgebra (resp. an algebra) in the same category. We have reproved this result by using specific definitions in terms of diagrams. These definitions are also used to prove such results for bra ..."
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Cited by 2 (2 self)
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It is known that if H is an algebra (resp. a coalgebra) in a rigid tensor category, then its dual H ∗ is a coalgebra (resp. an algebra) in the same category. We have reproved this result by using specific definitions in terms of diagrams. These definitions are also used to prove such results
Results 1  10
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45,751