Related papers: Frobenius Objects in Cartesian Bicategories
It is known that the quantale of sup-preserving maps from a complete lattice to itself is a Frobenius quantale if and only if the lattice is completely distributive. Since completely distributive lattices are the nuclear objects in the…
A convenient bicategory of topological stacks is constructed which is both complete and Cartesian closed. This bicategory, called the bicategory of compactly generated stacks, is the analogue of classical topological stacks, but for a…
We provide three functorial extensions of the equivalence between localic etale groupoids and their quantales. The main result is a biequivalence between the bicategory of localic etale groupoids, with bi-actions as 1-cells, and a…
We associate a monoidal category $\mathcal{H}_B$, defined in terms of planar diagrams, to any graded Frobenius superalgebra $B$. This category acts naturally on modules over the wreath product algebras associated to $B$. To $B$ we also…
We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups…
Monoidal functors U:C --> M with left adjoints determine, in a universal way, monoids T in the category of oplax monoidal endofunctors on M. Such monads will be called bimonads. Treating bimonads as abstract "quantum groupoids" we derive…
Multiplier bimonoids (or bialgebras) in arbitrary braided monoidal categories are defined. They are shown to possess monoidal categories of comodules and modules. These facts are explained by the structures carried by their induced…
By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once…
Hopf algebroids are generalization of Hopf algebras over non-commutative base rings. It consists of a left- and a right-bialgebroid structure related by a map called the antipode. However, if the base ring of a Hopf algebroid is commutative…
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, A must in addition possess a reversion, i.e. an isomorphism…
We endow twisted tensor products with a natural notion of counit and comultiplication, and we provide sufficient and necessary conditions making the twisted tensor product a counital coassociative coalgebra. We then characterize when the…
Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the…
We define biprops as a generalization of coloured props and of symmetric weak multicategories. These are bicategories whose objects form a free monoid. They are equipped with some structure resembling a symmetric strict tensor product. We…
Given a bicategory C and a family W of arrows of C, we give conditions on the pair (C,W) that allow us to construct the bicategorical localization with respect to W by dealing only with the 2-cells, that is without adding objects or arrows…
The main purpose is to characterise continuous maps that are $n$-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius $n$-homomorphisms between two function spaces that correspond to…
In the present paper by Frobenius algebra Y we mean a finite dimensional algebra possessing an associative and invertible (nondegenerate) form a scalar product, referred to as the Frobenius structure. The nondegenerate form has an inverse.…
This paper proves three different coherence theorems for symmetric monoidal bicategories. First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes. Second, we show that this implies that the free…
Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally,…
We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…
The notion of a Frobenius submanifold - a submanifold of a Frobenius manifold which is itself a Frobenius manifold with respect to structures induced from the original manifold - is studied. Two dimensional submanifolds are particularly…