Tannaka duality for coalgebras over commutative rings

Daniel Schaeppi (ETHZ)

Tannaka duality concerns the study of the relationship between a "group-like" object (an ordinary group, a compact topological group, an algebraic group, a group scheme, a quantum group, etc.) and its category of representations. This category is equipped with certain additional structures (e.g. a tensor product). The basic observation of Tannaka duality is that one can often go in the other direction, i.e., one can associate a "group-like" object to a category equipped with suitable additional structures. One would then like to know to which extent these processes are inverse to each other. We study such questions in the context of coalgebras over arbitrary commutative rings, and we give two partial extensions of well-known results for coalgebras over fields.