Abstract
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 X→ and i(X→), the image of 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 X→ and i(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.
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