  We introduce the notion of a non-degenerate solution of the braid equation on
the incidence coalgebra of a locally finite order. Each one of these solutions
induce by restriction a non-degenerate set theoretic solution over the
underlying set. So, it makes sense to ask if a non-degenerate set theoretic
solution on the underlying set of a locally finite order extends to a
non-degenerate solution on its incidence coalgebra. In this paper we begin the
study of this problem.
