Preliminary Proceedings of the Workshop on Geometry and Topology in Concurrency GETCO ’ 05 San Francisco , California , USA , August 21 , 2005

Several categories of models for concurrency involving topology have been put forward in each of which a notion of fundamental category is defined. One of them, the category of pospaces, is canonically included in almost all the others. Given a pospace −→X and i(− →X ), the image of −→X by the inclusion i of PoTop in some of the other category in which the fundamental category is defined, it is then natural to ask how the fundamental categories of −→X and i(−→X ) are related. The answer to this question is one of the purposes along of this article. We introduce a general framework for categories in which a reasonable notion of fundamental categories can be defined.

[1]  Luca Aceto,et al.  The Quest for Equational Axiomatizations of Parallel Composition: Status and Open Problems , 2006, APC 25.

[2]  Eric Goubault,et al.  Algebraic topology and concurrency , 2006, Theor. Comput. Sci..

[3]  Lisbeth Fajstrup,et al.  Dipaths and dihomotopies in a cubical complex , 2005, Adv. Appl. Math..

[4]  R. J. V. Glabbeek.  On the Expressiveness of Higher Dimensional Automata: (Extended Abstract) , 2005, EXPRESS.

[5]  Ulrich Fahrenberg,et al.  A Category of Higher-Dimensional Automata , 2005, FoSSaCS.

[6]  P. Gaucher.  Flow does not Model Flows up to Weak Dihomotopy , 2004, Appl. Categorical Struct..

[7]  P. Gaucher.  Comparing globular complex and flow , 2003, math/0308063.

[8]  P. Gaucher.  A MODEL CATEGORY FOR THE HOMOTOPY THEORY OF CONCURRENCY , 2003, math/0308054.

[9]  P. Gaucher.  HOMOLOGICAL PROPERTIES OF NON-DETERMINISTIC BRANCHINGS AND MERGINGS IN HIGHER DIMENSIONAL AUTOMATA , 2003, math/0305169.

[10]  M. Grandis.  Directed homotopy theory, I. The fundamental category , 2001, math/0111048.

[11]  É. Goubault,et al.  Topological deformation of higher dimensional automata , 2001, math/0107060.

[12]  Lisbeth Fajstrup,et al.  Loops, ditopology and deadlocks , 2000, Mathematical Structures in Computer Science.

[13]  May,et al.  A Concise Course in Algebraic Topology , 1999 .

[14]  Glynn Winskel,et al.  Bisimulation from Open Maps , 1994, Inf. Comput..

[15]  Mogens Nielsen,et al.  Models for Concurrency , 1992 .

[16]  Vaughan R. Pratt,et al.  Modeling concurrency with geometry , 1991, POPL '91.

[17]  S. Smolka,et al.  Proceedings of the 7th International Workshop on Verification of Infinite-State Systems (INFINITY'05) , 2005 .

[18]  Eric Goubault,et al.  SOME GEOMETRIC PERSPECTIVES IN CONCURRENCY THEORY , 2003 .

[19]  Marco Grandis,et al.  Directed homotopy theory, I , 2003 .

[20]  L. Fajstrup.  DICOVERING SPACES , 2003 .

[21]  Concurrency Theory,et al.  Preliminary Proceedings of the Workshop on , 2003 .

[22]  Marco Grandis,et al.  CUBICAL SETS AND THEIR SITE , 2003 .

[23]  M. Grandis.  DIRECTED HOMOTOPY THEORY, II. HOMOTOPY CONSTRUCTS , 2002 .

[24]  Philippe Gaucher,et al.  From Concurrency to Algebraic Topology , 2000, GETCO.

[25]  M. Osborne.  Basic Homological Algebra , 2000 .

[26]  W. Dwyer,et al.  Homotopy theories and model categories , 1997 .

[27]  É. Goubault.  Geometrie du parallelisme , 1995 .

[28]  L. Lewis.  The stable category and generalized Thom spectra , 1978 .

[29]  Revaz Valerianovich Gamkrelidze,et al.  Topology and Geometry , 1970 .

[30]  L. Nachbin.  Topology and order , 1965 .