  Combinatorial transgressions are secondary invariants of a space admitting
triangulations. They arise from subdivisions and are analogous to transgressive
forms such as those arising in Chern-Weil theory. Unlike combinatorial
characteristic classes, combinatorial transgressions have not been previously
studied. First, this article characterizes transgressions that are
path-independent of subdivision sequence. The result is obtained by using a
cohomology on posets that is shown to be equivalent to higher derived functors
of the inverse (or projective) limit over the opposite poset. Second, a
canonical local formula is demonstrated for a particular combinatorial
transgression: namely, that relative the difference of Poincar\'{e} duals to
the Euler class.
