%0 Journal Article %1 1059.55009 %A Grandis, Marco %D 2003 %J Cah. Topol. Géom. Différ. Catég. %K Homotopie gerichtete_Topologie %N 4 %P 281-316 %T Directed homotopy theory. I. %U http://www.numdam.org/numdam-bin/fitem?id=CTGDC_2003__44_4_281_0 %V 44 %X Looking at space-time models (and also at concurrency systems or traffic networks), one needs paths which can not be reversed. The answer is given by directed algebraic topology.This paper presents directed spaces, directed homotopy and their fundamental category (replacing the fundamental groupoid of ordinary spaces).More details and constructions are in a following work M. Grandis, Directed homotopy theory. II: Homotopy constructs, Theory Appl. Categ. 10, 369--391, electronic only (2002; Zbl 1034.55006).

@article{1059.55009, abstract = {{Looking at space-time models (and also at concurrency systems or traffic networks), one needs paths which can not be reversed. The answer is given by directed algebraic topology.\par This paper presents directed spaces, directed homotopy and their fundamental category (replacing the fundamental groupoid of ordinary spaces).\par More details and constructions are in a following work [{\it M. Grandis}, Directed homotopy theory. II: Homotopy constructs, Theory Appl. Categ. 10, 369--391, electronic only (2002; Zbl 1034.55006)].}}, added-at = {2012-08-01T17:19:02.000+0200}, author = {Grandis, Marco}, biburl = {https://www.bibsonomy.org/bibtex/260b08417a01cf476d2dea0c06b968d6b/keinstein}, classmath = {{*55U35 (Abstract homotopy theory)18G55 (Nonabelian homotopical algebra)55P99 (Homotopy theory)}}, file = {:Grandis/Directed Homotopy Theory, I.pdf:PDF;:Directed Homotopy Theory:PDF}, groups = {public}, interhash = {cb1b904a447740330a879472d77566fe}, intrahash = {60b08417a01cf476d2dea0c06b968d6b}, issn = {1245-530X}, journal = {Cah. Topol. Géom. Différ. Catég.}, keywords = {Homotopie gerichtete_Topologie}, language = {English}, number = 4, pages = {281-316}, reviewer = {{Georges Hoff (Villetaneuse)}}, timestamp = {2013-02-04T17:15:20.000+0100}, title = {{Directed homotopy theory. I.}}, url = {http://www.numdam.org/numdam-bin/fitem?id=CTGDC_2003__44_4_281_0}, username = {keinstein}, volume = 44, year = 2003 }