Re: localization : more precise question

I meant 'non-negative'. Maybe the definition of the category still needs to be debugged. I don't know. (The motivation of this question was to encode the notion of 1-dimensional HDA up to dihomotopy for those who know the subject in a "true" category such that isomorphism classes represent 1-dimensional HDA up to dihomotopy). "having a 'positive' derivative at all times" would be also sufficient I think.

I would like to add : I meant 'non-negative' locally. Because one needs that the morphism from an arrow a-->b to a loop a-->a exists. The exact definition is : morphism of local po-spaces (see "Algebraic topology and concurrency", by Fajstrup, Goubault & Rau{\ss}en ; preprint R-99-2008, Aalborg University). pg.