Lax -categories and directed homotopy
Cahiers de Topologie et Géométrie Différentielle Catégoriques (2006)
- Volume: 47, Issue: 2, page 107-128
- ISSN: 1245-530X
Access Full Article
topHow to cite
topGrandis, Marco. "Lax $2$-categories and directed homotopy." Cahiers de Topologie et Géométrie Différentielle Catégoriques 47.2 (2006): 107-128. <http://eudml.org/doc/91703>.
@article{Grandis2006,
author = {Grandis, Marco},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {2-categories; bicategories; lax categories; homotopy theory; directed algebraic topology; fundamental categories},
language = {eng},
number = {2},
pages = {107-128},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Lax $2$-categories and directed homotopy},
url = {http://eudml.org/doc/91703},
volume = {47},
year = {2006},
}
TY - JOUR
AU - Grandis, Marco
TI - Lax $2$-categories and directed homotopy
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2006
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 47
IS - 2
SP - 107
EP - 128
LA - eng
KW - 2-categories; bicategories; lax categories; homotopy theory; directed algebraic topology; fundamental categories
UR - http://eudml.org/doc/91703
ER -
References
top- [1] A. Bauer - L. Birkedal - D.S. Scott, Equilogical spaces, TheoreticalComputer Science315 (2004), 35-59. Zbl1059.18004MR2072989
- [2] J. Bénabou, Introduction to bicategories, in: Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, Vol. 47, Springer, Berlin1967, pp. 1-77. MR220789
- [3] F. Borceux, Handbook of categorical algebra, Vol. 1, Cambridge University Press, Cambridge1994. Zbl0803.18001
- [4] M.C. Bunge, Coherent extensions and relational algebras, Trans. Amer. Math. Soc.197 (1974), 355-390. Zbl0358.18004MR344305
- [5] A. Burroni, T-categories, Cah. Topol. Géom. Différ.12 (1971), 215-321. Zbl0246.18007
- [6] E. Cheng - A. Lauda, Higher-dimensional categories: an illustrated guide book, draft version, revised 2004. http://www.math.uchicago.edu/-eugenia/guidebook/index.html
- [7] C. Ehresmann, Catégories structurées, Ann. Sci. Ecole Norm. Sup.80 (1963), 349-425. Zbl0128.02002MR197529
- [8] C. Ehresmann, Catégories et structures, Dunod, Paris1965. Zbl0192.09803MR213410
- [9] L. Fajstrup, M. Raussen, E. Goubault, E. Haucourt, Components of the fundamental category, Appl. Categ. Structures12 (2004), 81-108. Zbl1078.55020MR2057412
- [10] E. Goubault, Geometry and concurrency: a user's guide, in: Geometry and concurrency, Math. Structures Comput. Sci.10 (2000), no. 4, pp. 411-425. Zbl0956.68517MR1786469
- [11] M. Grandis, Directed homotopy theory, I. The fundamental category, Cah. Topol. Géom. Différ. Catég.44 (2003), 281-316. Zbl1059.55009MR2030049
- [12] M. Grandis, Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology), Math. Proc. Cambridge Philos. Soc.138 (2005), 233-262. Zbl1068.55004MR2132167
- [13] M. Grandis, Inequilogical spaces, directed homology and noncommutative geometry, Homology Homotopy Appl.6 (2004), 413-437. Zbl1079.18001MR2118494
- [14] M. Grandis, The shape of a category up to directed homotopy, Theory Appl. Categ.15 (2005) (CT2004), No. 4, 95-146. Zbl1091.55006MR2210577
- [15] M. Grandis, Modelling fundamental 2-categories for directed homotopy, Homology Homotopy Appl., to appear. [Dip. Mat. Univ. Genova, Preprint 527 (2005) http://www.dima.unige.it/-grandis/Shp2.pdf] Zbl1087.18005MR2205214
- [16] G.M. Kelly, On Mac Lane's conditions for coherence of natural associativities, commutativities, etc., J. Algebra1 (1964), 397-402. Zbl0246.18008MR182649
- [17] T. Leinster, Higher operads, higher categories, Cambridge University Press, Cambridge2004. Zbl1160.18001MR2094071
- [18] S. Mac Lane, Natural associativity and commutativity, Rice Univ. Studies49 (1963), 28-46. Zbl0244.18008MR170925
- [19] D. Scott, A new category? Domains, spaces and equivalence relations, Unpublished manuscript (1996). http://www.cs.cmu.edu/Groups/LTC/
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.