The preprint described below is available, in pdf. I would like to have information on other works considering *absolute* comparison cells/constraints, in weak or lax structures. Best wishes to all colleagues and friends Marco Grandis _______________ M. Grandis, Absolute lax 2-categories Dip. Mat. Univ. Genova, Preprint 533 (2005), 22 p. http://www.dima.unige.it/~grandis/LCat2.pdf Abstract. We have introduced, in a previous paper, the fundamental lax 2-category of a 'directed space' X. Here we show that, when X has a T1-topology, this structure can be embedded into a larger one, with the same objects (the points of X), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells are *absolute*, in the sense that they only depend on the arrows themselves rather than on their syntactic expression, as in the usual settings of lax or weak structures. It follows that, in the original structure, all the diagrams of comparison cells commute, even if not constructed in a natural way and even if the composed cells need not stay within the old system. ____ The previous preprint mentioned above ('Lax 2-categories and directed homotopy') is also available, at: http://www.dima.unige.it/~grandis/LCat.pdf ____ Dipartimento di Matematica Universita` di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/