# Lie 2-Algebras

@article{Crans2004Lie2, title={Lie 2-Algebras}, author={Alissa S. Crans}, journal={arXiv: Quantum Algebra}, year={2004} }

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 category of vector spaces. We then define a `semistrict Lie 2-algebra' to be a 2-vector space equipped with a skew-symmetric bilinear functor satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its own. Much of…

## 52 Citations

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