Braided Deformations of Monoidal Categories and Vassiliev Invariants

Details Braided Deformations of Monoidal Categories and Vassiliev Invariants Braided Deformations of Monoidal Categories and Vassiliev Invariants

1997-10-06

arxiv.org/abs/q-alg/9710010v1

Mathematics

Quantum Algebra

LaTeX 2.1, uses amssym.def and amssym, 20 pages, all figures in LaTeX

Scientific paper

Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev invariants. The deformation theory of braidings is subsumed by the deformation theory of monoidal functors, which proves surprisingly rich: the deformation complex of a monoidal functor has the same structure as the deformation complex of an algebra, including a pre-Lie structure, from which it is see that the problem of deforming monoidal functors (including braidings) is purely cohomological in nature.

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