Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories
Category Theory
2009-03-03 v1 Quantum Algebra
Abstract
We introduce a variant on the graphical calculus of Cockett and Seely for monoidal functors and illustrate it with a discussion of Tannaka reconstruction, some of which is known and some of which is new. The new portion is: given a separable Frobenius functor F: A --> B from a monoidal category A to a suitably complete or cocomplete braided autonomous category B, the usual formula for Tannaka reconstruction gives a weak bialgebra in B; if, moreover, A is autonomous, this weak bialgebra is in fact a weak Hopf algebra.
Keywords
Cite
@article{arxiv.0903.0208,
title = {Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories},
author = {Micah Blake McCurdy},
journal= {arXiv preprint arXiv:0903.0208},
year = {2009}
}
Comments
16 pages, a great many figures