# A categorical proof of the Parshin reciprocity laws on algebraic surfaces

@inproceedings{Osipov2011ACP,
title={A categorical proof of the Parshin reciprocity laws on algebraic surfaces},
author={Denis Osipov and X Zhu},
year={2011}
}
We define and study the 2-category of torsors over a Picard groupoid, a central extension of a group by a Picard groupoid, and commutator maps in this central extension. Using this in the context of two-dimensional local fields and two-dimensional adèle theory we obtain the two-dimensional tame symbol and a new proof of Parshin reciprocity laws on an algebraic surface.