Towards the Theory of Non--Abelian Tensor Fields I

We present a triangulation–independent area–ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two–form connection'' should carry three color’’ indices rather than two as it is in the case of the ordinary one–form gauge connection. To define the prescription in question we have to define how to {\it exponentiate} a matrix with three indices. The definition uses the fusion rule structure constants.