  In p-form lattice gauge theory, the fluctuating variables live on
p-dimensional cells and interact around (p+1)-dimensional cells. It has been
argued that the continuum version of this model should be described by
(p-1)-gerbes. However, only connections and curvatures for gerbes are
understood, not covariant derivatives. Using the lattice analogy, an
alternative definition of gerbes is proposed: sections are functions phi(x,s),
were x is the base point and s is the surface element. In this purely local
formalism, there is a natural covariant derivative. The Yang-Baxter equation,
and more generally the simplex equations, arise as zero-curvature conditions.
The action of algebras of vector fields and gerbe gauge transformations, and
their abelian extensions, are described.
