Reconstruction in braided categories and a notion of commutative bialgebra

✍ Scribed by Martin Neuchl; Peter Schauenburg

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 829 KB
• Volume: 124
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00093-x

✦ Synopsis

A braided group in the sense of Majid [6] is a Hopf algebra B in a braided monoidal category which satisfies a generalized commutativity condition; this condition is expressed with respect to a certain class of B-comodules. The more obvious condition that B be a commutative algebra in the braided category does not make sense.

We propose a different commutativity condition for bialgebras: We show that a coalgebra reconstructed from a category over a braided base category d has the additional structure of being an object of the center ~e(~'-Coalg) of the category of coalgebras. We prove that braided groups which are reconstructed from braided monoidal categories over ~¢ are commutative algebras in the center of •-Coalg. We give further information about Hopf algebras in :Y'(d-Coalg).