An alternative description of braided monoidal categories
Category Theory
2013-07-24 v1 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital case, the coherence conditions for a b-structure are shown to be equivalent to the usual associativity, unit and braiding axioms. We also discuss the next dimensional version, that is, b-structures on bicategories. As an application, we show how special b-categories result in the Yang-Baxter equation, and how special b-bicategories produce Zamolodchikov's tetrahedron equation. Finally, we define a cohomology theory (the b-cohomology) which plays a role analogous to the one abelian group cohomology has for braided monoidal categories.
Cite
@article{arxiv.1307.5969,
title = {An alternative description of braided monoidal categories},
author = {Alexei Davydov and Ingo Runkel},
journal= {arXiv preprint arXiv:1307.5969},
year = {2013}
}