In this survey talk, we review the basics of the Tannaka-Krein reconstruction formalism in detail. Both the abelian
and the monoidal setting will be considered, and emphasis is placed on the following problem: given an algebraic
object of interest (typically a Hopf algebra), how can we describe its (derived) category of representations using
monoidal categories defined via generators and relations.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312