  We give a construction of the two-dimensional tame symbol as the commutator
of a group-like monoidal groupoid which is obtained from some group of k-linear
operators acting in a two-dimensional local field and corresponds to some third
cohomology class of this group. We give also the hypothetical method for the
proof of the two-dimensional Parshin reciprocity laws.
  This text was written in 2003 as preprint 03-13 of the Humboldt University of
Berlin and was available at
http://edoc.hu-berlin.de/docviews/abstract.php?id=26204 (only evident misprints
are corrected now). Later E. Frenkel and X. Zhu obtained in arXiv:0810.1487
[math.RT] more general results concerning the third cohomology classes of
groups acting on two-dimensional local fields, and the author and X. Zhu
obtained in arXiv:1002.4848 [math.AG] the proof of the Parshin reciprocity laws
on an algebraic surface similar to the Tate proof of the residue formula on an
algebraic curve.
