50 citations · 276 across the 16 of their papers we have counts for
19 papers
Grothendieck-Verdier module categories, Frobenius algebras and relative Serre functors
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert +1
We develop the theory of module categories over a Grothendieck-Verdier category, i.e. a monoidal category with a dualizing object and hence a duality structure more general than ri…
Fusion Quivers
Gregor Schaumann
We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a larg…
Grothendieck-Verdier duality in categories of bimodules and weak module functors
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert +1
Various monoidal categories, including suitable representation categories of vertex operator algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a…
Reshetikhin-Turaev TQFTs close under generalised orbifolds
Nils Carqueville, Vincentas Mulevicius, Ingo Runkel +2
We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al., arXiv:2101.02482 to Reshetikhin-Turaev defect TQFTs. We explain that the modular fusion cat…
Orbifold graph TQFTs
Nils Carqueville, Vincentas Mulevicius, Ingo Runkel +2
A generalised orbifold of a defect TQFT is another TQFT obtained by performing a state sum construction internal to . As an i…
Module Eilenberg-Watts calculus
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
The categorical formulation of the Eilenberg-Watts calculus relates, for any pair of finite categories M and N, the finite categories Fun^{le}(N,M) and Fun^{re}(N,M) of linear left…
A modular functor from state sums for finite tensor categories and their bimodules
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defin…
Orbifolds of Reshetikhin-Turaev TQFTs
Nils Carqueville, Ingo Runkel, Gregor Schaumann
We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a modular tensor category , using the language of defect TQFT from [arXiv:1705.060…
Eigenvalues of the squared antipode in finite dimensional weak Hopf algebras
Pavel Etingof, Gregor Schaumann
We extend Schaumann's theory of pivotal structures on fusion categories matched to a module category and of module traces developed in arXiv:1206.5716 to the case of non-semisimple…
The logarithmic Cardy case: Boundary states and annuli
Jürgen Fuchs, Terry Gannon, Gregor Schaumann +1
We present a model-independent study of boundary states in the Cardy case that covers all conformal field theories for which the representation category of the chiral algebra is a…
Line and surface defects in Reshetikhin-Turaev TQFT
Nils Carqueville, Ingo Runkel, Gregor Schaumann
A modular tensor category gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{…
Orbifolds of n-dimensional defect TQFTs
Nils Carqueville, Ingo Runkel, Gregor Schaumann
We introduce the notion of -dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension . T…
Eilenberg-Watts calculus for finite categories and a bimodule Radford theorem
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact fu…
3-dimensional defect TQFTs and their tricategories
Nils Carqueville, Catherine Meusburger, Gregor Schaumann
We initiate a systematic study of 3-dimensional `defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms.…
A trace for bimodule categories
Jurgen Fuchs, Gregor Schaumann, Christoph Schweigert
We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued tra…
Pivotal tricategories and a categorification of inner-product modules
Gregor Schaumann
This article investigates duals for bimodule categories over finite tensor categories. We show that finite bimodule categories form a tricategory and discuss the dualities in this…
Gray categories with duals and their diagrams
John W. Barrett, Catherine Meusburger, Gregor Schaumann
The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a c…
Traces on Module Categories over Fusion Categories
Gregor Schaumann
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 c…
Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds
Stefan Jansen, Nikolai Neumaier, Gregor Schaumann +1
In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We co…