caa a22 4500 46788255X CHVBK 20180406152724.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10485-006-9017-8 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9017-8 Grandis Marco Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy aut Absolute Lax 2-categories [Elektronische Daten] [Marco Grandis] 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 $T_1$ -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. Springer Science+Business Media B.V., 2006 2-categories nationallicence bicategories nationallicence lax 2-categories nationallicence homotopy theory nationallicence directed algebraic topology nationallicence fundamental categories nationallicence Applied Categorical Structures Kluwer Academic Publishers 14/3(2006-06-01), 191-214 0927-2852 14:3<191 2006 14 10485 https://doi.org/10.1007/s10485-006-9017-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9017-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Grandis Marco Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/3(2006-06-01), 191-214 0927-2852 14:3<191 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer