About the globular homology of higher dimensional automata
Cahiers de Topologie et Géométrie Différentielle Catégoriques (2002)
- Volume: 43, Issue: 2, page 107-156
- ISSN: 1245-530X
Access Full Article
topHow to cite
topGaucher, Philippe. "About the globular homology of higher dimensional automata." Cahiers de Topologie et Géométrie Différentielle Catégoriques 43.2 (2002): 107-156. <http://eudml.org/doc/91655>.
@article{Gaucher2002,
author = {Gaucher, Philippe},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {higher-dimensional automaton; globular homology; corner homology; omega-category; concurrency},
language = {eng},
number = {2},
pages = {107-156},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {About the globular homology of higher dimensional automata},
url = {http://eudml.org/doc/91655},
volume = {43},
year = {2002},
}
TY - JOUR
AU - Gaucher, Philippe
TI - About the globular homology of higher dimensional automata
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2002
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 43
IS - 2
SP - 107
EP - 156
LA - eng
KW - higher-dimensional automaton; globular homology; corner homology; omega-category; concurrency
UR - http://eudml.org/doc/91655
ER -
References
top- [1] Fahd A. A. Al-Agl.Aspects of multiple categories. PhD thesis, University of Wales, Department of Pure Mathematics, University College of North Wales, Bangor, Gwynedd LL57 1UT, U.K., September 1989.
- [2] H.J. Baues.Geometry of loop spaces and the cobar construction. Mem. Amer: Math. Soc., 25(230):ix+171, 1980. Zbl0473.55009MR567799
- [3] R. Brown and P.J. Higgins.The equivalence of ∞-groupoids and crossed complexes. Cahiers Topologie Géom. Differentielle, 22(4):371-386, 1981. Zbl0487.55007
- [4] R. Brown and P.J. Higgins.On the algebra of cubes. J. Pure Appl. Algebra, 21 (3):233-260, 1981. Zbl0468.55007MR617135
- [5] J. Duskin.Simplicial methods and the interpretation of "triple" cohomology. Mem. Amer. Math. Soc., 3(issue 2, 163):v+135, 1975. Zbl0376.18011MR393196
- [6] L. Fajstrup, E. Goubault, and M. Raussen.Algebraic topology and concurrency. preprint, 1998. Zbl1099.55003MR2242768
- [7] L. Fajstrup, E. Goubault, and M. Raußen.Detecting deadlocks in concurrent systems. In CONCUR'98: concurrency theory (Nice), pages 332-347. Springer, Berlin, 1998. MR1683333
- [8] P. Gaucher.Combinatorics of branchings in higher dimensional automata. preprint math.CT/9912059, 2000. MR1847036
- [9] P. Gaucher.Homotopy invariants of higher dimensional categories and concurrency in computer science. Math. Structures Comput. Sci., 10(4):481-524, 2000. Geometry and concurrency. Zbl0956.68097MR1786472
- [10] P. Gaucher.From concurrency to algebraic topology. In Jeremy Gunawardena Maurice Herlihy Martin Raussen Patrick Cousot, Eric Goubault and Vladimiro Sassone, editors, Electronic Notes in Theoretical Computer Science, volume 39. Elsevier Science Publishers, 2001. Zbl0976.68069MR2186520
- [11] E. Goubault.The Geometry of Concurrency. PhD thesis, Ecole Nor-male Supérieure, 1995.
- [12] M. Johnson.The combinatorics of n-categorical pasting. J. Pure Appl. Algebra, 62(3):211-225, 1989. Zbl0694.18007MR1026875
- [13] K.H. Kamps and T. Porter.Abstract homotopy and simple homotopy theory. World Scientific Publishing Co. Inc., River Edge, NJ, 1997. Zbl0890.55014MR1464944
- [14] M. Kapranov and V. Voevodsky.Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results). Cahiers Topologie Geom. Differentielle Catégoriques, 32(1):11-27, 1991. International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990). Zbl0748.18010MR1130400
- [15] S. Mac Lane.Categories for the working mathematician. Springer-Verlag, New York, second edition, 1998. Zbl0906.18001MR1712872
- [16] Yu. I. Manin and V.V. Schechtman.Arrangements of hyperplanes, higher braid groups and higher Bruhat orders. In Algebraic number theory, pages 289-308. Academic Press, Boston, MA, 1989. Zbl0759.20002MR1097620
- [17] J.P. May.Simplicial Objects in Algebraic Topology. D. Van Nostrand Company, 1967. Zbl0165.26004MR222892
- [18] R.J. Milgram.Iterated loop spaces. Ann. of Math. (2), 84:386-403, 1966. Zbl0145.19901MR206951
- [19] V. Pratt.Modeling concurrency with geometry. In ACM Press, editor, Proc. of the 18th ACM Symposium on Principles of Programming Languages, 1991.
- [20] D. Quillen.Higher algebraic K-theory. I. pages 85-147. Lecture Notes in Math., Vol. 341, 1973. Zbl0292.18004MR338129
- [21] S. Sokolowski.Classifying holes of arbitrary dimensions in partially ordered cubes. Technical report, Kansas State University, 1999.
- [22] R. Steiner.Tensor products of infinity-categories. University of Glasgow, 1991.
- [23] R. Street.The algebra of oriented simplexes. J. Pure Appl. Algebra, 49(3):283-335, 1987. Zbl0661.18005MR920944
- [24] R. Street.Fillers for nerves. In Categorical algebra and its applications (Louvain-La-Neuve, 1987), pages 337-341. Springer, Berlin, 1988. Zbl0656.18012MR975981
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.