24 citations · 77 across the 18 of their papers we have counts for
6 papers · 1 filter
Crossed modules of racks
Alissa S. Crans, Friedrich Wagemann
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-lik…
Cohomology of Frobenius Algebras and the Yang-Baxter Equation
J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi +2
A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on defo…
Cohomology of the adjoint of Hopf algebras
J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi +1
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group al…
From Loop Groups to 2-Groups
John C. Baez, Alissa S. Crans, Danny Stevenson +1
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group . A Lie 2-algebra is a categorified v…
Lie 2-Algebras
Alissa S. Crans
We categorify the theory of Lie algebras beginning with a new notion of categorified vector space, or `2-vector space', which we define as an internal category in Vect, the categor…
Higher-Dimensional Algebra VI: Lie 2-Algebras
John C. Baez, Alissa S. Crans
The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having t…