383 citations · 3.5k across the 90 of their papers we have counts for
10 papers · 1 filter
Crossed-module crossed braided categories
Azat M. Gainutdinov, Ingo Runkel, Bangxin Wang
For a crossed module , we introduce the notion of -crossed braided (resp. ribbon) categories, where the categories are graded by group and carry an -action. O…
An alternative description of braided monoidal categories
Alexei Davydov, Ingo Runkel
We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital cas…
Module categories for permutation modular invariants
Till Barmeier, Jurgen Fuchs, Ingo Runkel +1
We show that a braided monoidal category C can be endowed with the structure of a right (and left) module category over C \times C. In fact, there is a family of such module catego…
On the Rosenberg-Zelinsky sequence in abelian monoidal categories
Till Barmeier, J"urgen Fuchs, Ingo Runkel +1
We consider Frobenius algebras and their bimodules in certain abelian monoidal categories. In particular we study the Picard group of the category of bimodules over a Frobenius alg…
Morita classes of algebras in modular tensor categories
Liang Kong, Ingo Runkel
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 centr…
The fusion algebra of bimodule categories
Jurgen Fuchs, Ingo Runkel, Christoph Schweigert
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appro…
Categorification and correlation functions in conformal field theory
Ingo Runkel, Jurgen Fuchs, Christoph Schweigert
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional…
Topological and conformal field theory as Frobenius algebras
Ingo Runkel, Jens Fjelstad, Jurgen Fuchs +1
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of wor…
Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions
Jurgen Fuchs, Ingo Runkel, Christoph Schweigert
A Morita class of symmetric special Frobenius algebras A in the modular tensor category of a chiral CFT determines a full CFT on oriented world sheets. For unoriented world sheets,…
Correspondences of ribbon categories
J"urg Fr"ohlich, J"urgen Fuchs, Ingo Runkel +1
Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tenso…