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Abstract: One can associate to any strict globular omega-category three augmented simplicial nerves called the globular nerve, the branching and the merging semi-cubical nerves. If this strict globular omega-category is freely generated by a precubical set, then the corresponding homology theories contain different informations about the geometry of the higher dimensional automaton modeled by the precubical set. Adding inverses in this omega-category to any morphism of dimension greater than 2 and with... (Update)
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...This section focuses on a very striking one. The fundamental algebraic structure which has emerged from the categorical approach [Gau00c, Gau00a, Gau01b] is the diagram of Figure 11 where C is an category. The analogue in the globular CW complex framework is the diagram of...
...and transitive closure of f(x; x 0 y) x; y; x 0 y 2 PCg (resp. f(y; x 0 y) x; y; x 0 y 2 PCg) in PC PC. Proposition 3.2. [Gau01d] Let 2 f; g and let C be a non contracting category. Then the universal problem There exists a pair (D; such that D is an...
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BibTeX entry: (Update)
P. Gaucher. The branching nerve of HDA and the Kan condition, 2001. http://citeseer.ist.psu.edu/gaucher03branching.html More
@misc{ gaucher01branching,
author = "P. Gaucher",
title = "The branching nerve of HDA and the Kan condition",
text = "P. Gaucher. The branching nerve of HDA and the Kan condition, 2001.",
year = "2001",
url = "citeseer.ist.psu.edu/gaucher03branching.html" }
Citations (may not include all citations):562 Categories for the working mathematician (context) - Lane - 1998
96 Simplicial objects in algebraic topology (context) - May - 1967
54 Modeling concurrency with geometry - Pratt - 1991
33 The algebra of oriented simplexes (context) - Street - 1987
23 the algebra of cubes (context) - Brown, Higgins - 1981
21 Homotopy invariants of higher dimensional categories and con.. - Gaucher - 2000
20 Ecole Normale Superieure (context) - Goubault, of et al. - 1995
10 About the globular homology of higher dimensional automata - Gaucher - 2002
9 Cahiers Topologie Geom (context) - Brown, Higgins et al. - 1981
8 From concurrency to algebraic topology - Gaucher - 2000
8 Combinatorics of branchings in higher dimensional automata - Gaucher - 2001
7 Tensor products of infinity-categories (context) - Steiner - 1991
7 The petit topos of globular sets (context) - Street - 2000
5 Pasting in multiple categories - Steiner - 1998
4 Implementing a static analyzer of concurrent programs: Probl.. - Cridlig - 1996
4 A Convenient Category for The Homotopy Theory of Concurrency (context) - Gaucher
2 Approche polygraphique des non strictes (context) - Penon - 1999
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