Comparing Topological Models for Concurrency

Several categories of models for concurrency involving topology have been put forward in each of which a notion of fundamental category is defined. One of them, the category of pospaces, is canonically included in almost all the others. Given a pospace over(X, →) and i (over(X, →)), the image of over(X, →) by the inclusion i of PoTop in some of the other category in which the fundamental category is defined, it is then natural to ask how the fundamental categories of over(X, →) and i (over(X, →)) are related. The answer to this question is one of the purposes along of this article. We introduce a general framework for categories in which a reasonable notion of fundamental categories can be defined.