  We focus on working on incidence rings and their group of units. Some general
properties about them are given, including how they are always the inverse
limit of finite matrix groups/rings, giving a natural way to define their
topology. Such construction can also be translated as a functor from the
category of locally finite, preordered sets to the category of topological
rings. It is shown that under some assumptions on the ordered sets, simple
matrix groups over a field can be built from the group of units of such rings.
