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 and , the image of 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 and 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.