2003/01/22 by K. Szlachanyi, Szlachanyi, K.
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0301253
16 pp, AMS Latex, Talk given at "Hopf Algebras in Noncommutative Geometry and Physics", Brussels, June, 2002
arxiv created 2003/01/22 · arxiv updated 2009/11/30
Every monoidal functor G: C --> M has a canonical factorization through the category of bimodules over some monoid R in M such that the factor U: C -->R MR is strongly unital. Using this result and the characterization of the forgetful functors MA -->R MR of bialgebroids A over R given by Schauenburg together with their bimonad description given by the author recently here we characterize the "long" forgetful functors MA -->R MR --> M of both bialgebroids and weak bialgebras.