## A first attempt to describe the fundamental category of a po-space

### Eric Goubault – 18 December 2002

In this last talk, I will come back to ground level, and try to "compute" some fundamental categories in some fairly simple cases, but still of some value on the computer-scientific side. The idea is that the fundamental category is "essentially finite" in some nice cases, and that we ought to be able to describe it by some kind of generators and relations. This reduction to finite information, when possible, is done through various categories of fractions constructions. This could also be seen as a first attempt to understand a bit better the T-homotopy in Flow (of P. Gaucher). This is work (joint with M. Raussen, L. Fajstrup and E. Haucourt) in progress, and is certainly not polished at all, all comments will be \ gratefully acknowledged.

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