Higher dimensional algebra V: 2-groups (2009)
A 2-group is a ‘categorified ’ version of a group, in which the underlying set G has been replaced by a category and the multiplication map m: G×G → G has been replaced by a functor. Various...
Crystals from categorified quantum groups (2009)
Lauda, Aaron D., Vazirani, Monica
We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify...
Nilpotency in type A cyclotomic quotients (2009)
We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl(k).
Open-closed TQFTs extend Khovanov homology from links to tangles (2009)
Lauda, Aaron D., Pfeiffer, Hendryk
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not...
A diagrammatic approach to categorification of quantum groups III (2008)
Khovanov, Mikhail, Lauda, Aaron D.
We categorify the idempotented form of quantum sl(n).
A diagrammatic approach to categorification of quantum groups II (2008)
Khovanov, Mikhail, Lauda, Aaron D.
We categorify one-half of the quantum group associated to an arbitrary Cartan datum.
A diagrammatic approach to categorification of quantum groups I (2008)
Khovanov, Mikhail, Lauda, Aaron D.
To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify $U^-_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Kac-Moody...
Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties (2008)
A 2-category was introduced in arXiv:0803.3652 [math.QA] that categorifies Lusztig's integral version of quantum sl(2). Here we construct for each positive integer N arepresentation of this...
A categorification of quantum sl(2) (2008)
We categorify Lusztig's version of the quantized enveloping algebra for sl(2). Using a graphical calculus a 2-category is constructed whose split Grothendieck ring is isomorphic to Lusztig's algebra....
Frobenius algebras and ambidextrous adjunctions (2008)
Abstract. In this paper we explain the relationship between Frobenius objects inmonoidal categories and adjunctions in 2-categories. Specifically, we show that every Frobenius object in a monoidal...
Frobenius algebras and ambidextrous adjunctions (2008)
Abstract. In this paper we explain the relationship between Frobenius objects in monoidal categories and adjunctions in 2-categories. Specifically, we show that every Frobenius object in a monoidal...
Open-closed strings: Two-dimensional open-closed TQFTs and knowledgeable Frobenius algebras (2008)
Lauda, Aaron D., Pfeiffer, Hendryk
We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth...
State sum construction of two-dimensional open-closed topological quantum field theories (2007)
Lauda, Aaron D., Pfeiffer, Hendryk
We present a state sum construction of two-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, which generalizes the state sum of Fukuma--Hosono--Kawai from...
Open-closed TQFTs extend Khovanov homology from links to tangles (2006)
Lauda, Aaron D., Pfeiffer, Hendryk
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not...
State sum construction of two-dimensional open-closed Topological Quantum Field Theories (2006)
Lauda, Aaron D., Pfeiffer, Hendryk
We present a state sum construction of two-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, which generalizes the state sum of Fukuma--Hosono--Kawai from...
Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras (2005)
Lauda, Aaron D., Pfeiffer, Hendryk
We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth...
Frobenius algebras and planar open string topological field theories (2005)
Motivated by the Moore-Segal axioms for an open-closed topological field theory, we consider planar open string topological field theories. We rigorously define a category 2Thick whose objects and...
Frobenius algebras and ambidextrous adjunctions (2005)
In this paper we explain the relationship between Frobenius objects in monoidal categories and adjunctions in 2-categories. In particular, we show that every Frobenius object in a monoidal category M...
Higher-Dimensional Algebra V: 2-Groups (2003)
Baez, John C., Lauda, Aaron D.
A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various versions of this...
A 2-group is a `categorified' version of a group, in which the underlying set G has been replaced by a category and the multiplication map m: G x G -> G has been replaced by a functor. A number of...
Two-dimensional open-closed TQFTs and knowledgeable Frobenius algebras
Lauda,Aaron D., Pfeiffer,Hendryk
We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth...