A balanced coalgebroid is a ${\cal V}^{op}$-category with extra structure ensuring that its category of representations is a balanced monoidal category. We show, in a sense to be made precise, that a balanced structure on a coalgebroid may be reconstructed from the corresponding structure on its category of representations. This includes the reconstruction of dual quasi-bialgebras, quasi-triangular dual quasi-bialgebras, and balanced quasi-triangular dual quasi-bialgebras; the latter of which is a quantum group when equipped with a compatible antipode. As an application we construct a balanced coalgebroid whose category of representations is equivalent to the symmetric monoidal category of chain complexes. The appendix provides the definitions of a braided monoidal bicategory and sylleptic monoidal bicategory.
Keywords: Symmetric monoidal bicategories, balanced Vop-categories, coalgebras, quantum groups.
@article{TAC_2000_7_a5,
author = {Paddy McCrudden},
title = {Balanced {Coalgebroids}},
journal = {Theory and applications of categories},
pages = {71--147},
year = {2000},
volume = {7},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a5/}
}
Paddy McCrudden. Balanced Coalgebroids. Theory and applications of categories, Tome 7 (2000), pp. 71-147. http://geodesic.mathdoc.fr/item/TAC_2000_7_a5/