The Higher YM theories generalize these of the standard model of particles. From the string theory side, the geometrical constructions of gerbes appear, when describing non-vanishing B-fields on branes. Both, higher YM and gerbes are proved to be the same mathematical object. Thus, a natural candidate for the intermediate stage of the compactification in string theory appears. Moreover, replacing smooth 2-spaces by some categories of smooth topoi gives rise to the generalized spacetime based on topoi.

PACS numbers: 11.15.--q, 02.10.--v