Directed homotopy theory, I

Marco Grandis

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2003)

  • Volume: 44, Issue: 4, page 281-316
  • ISSN: 1245-530X

How to cite

top

Grandis, Marco. "Directed homotopy theory, I." Cahiers de Topologie et Géométrie Différentielle Catégoriques 44.4 (2003): 281-316. <http://eudml.org/doc/91674>.

@article{Grandis2003,
author = {Grandis, Marco},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {homotopy theory; directed homotopy; directed space; fundamental category},
language = {eng},
number = {4},
pages = {281-316},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Directed homotopy theory, I},
url = {http://eudml.org/doc/91674},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Grandis, Marco
TI - Directed homotopy theory, I
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2003
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 44
IS - 4
SP - 281
EP - 316
LA - eng
KW - homotopy theory; directed homotopy; directed space; fundamental category
UR - http://eudml.org/doc/91674
ER -

References

top
  1. [1] F. Borceux, Handbook of categorical algebra 1-3, Cambridge University Press, Cambridge1994. Zbl0911.18001MR1291599
  2. [2] N. Bourbaki, Topologie générale, Ch. 10, Hermann, Paris1961. 
  3. [3] R. Brown, Topology, Ellis Horwood, Chichester1988. Zbl0655.55001MR984598
  4. [4] R. Brown - P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra21 (1981), 233-260. Zbl0468.55007MR617135
  5. [5] E.B. Curtis, Simplicial homotopy theory, Adv. Math.6 (1971), 107-209. Zbl0225.55002MR279808
  6. [6] L. Fajstrup - E. Goubault - M. Raussen, Algebraic topology and concurrency, Preprint 1999. MR2242768
  7. [7] P. Gaucher, Homotopy invariants of higher dimensional categories and concurrency in computer science, Math. Struct. in Comp. Science10 (2000), 481-524. Zbl0956.68097MR1786472
  8. [9] P. Gaucher - E. Goubault, Topological deformation of higher dimensional automata, Preprint 2001. http://arXiv.org/abs/math.AT/0107060 Zbl1030.68058
  9. [9] 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
  10. [10] M. Grandis, Cubical homotopical algebra and cochain algebras, Ann. Mat. Pura Appl.170 (1996) 147-186. Zbl0871.55016MR1441618
  11. [11] M. Grandis, Categorically algebraic foundations for homotopical algebra, Appl. Categ. Structures5 (1997), 363-413. Zbl0906.55015MR1478526
  12. [12] M. Grandis, Higher fundamental functors for simplicial sets, Cahiers Topologie Géom. Diff. Catég.42 (2001), 101-136. Zbl1006.18014MR1839359
  13. [13] M. Grandis, Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency, Preprint 2001. http://www.dima.unige.it/~grandis/ MR1994944
  14. [14] M. Grandis, Directed homotopy theory, II. Homotopy constructs, Dip. Mat. Univ. Genova, Preprint 446 (2001). http://www.dima.unige.it/-grandis/ MR1921751
  15. [15] K.H. Kamps - T. Porter, Abstract homotopy and simple homotopy theory, World Scientific Publishing Co., River Edge, NJ1997. Zbl0890.55014MR1464944
  16. [16] D.M. Kan, Abstract homotopy, II, Proc. Nat. Acad. Sci. U.S.A.42 (1956), 255-258. Zbl0071.16702MR79763
  17. [17] J.C. Kelly, Bitopological spaces, Proc. London Math. Soc.13 (1963), 71-89. Zbl0107.16401MR143169
  18. [18] F.W. Lawvere, Metric spaces, generalized logic and closed categories, Rend-Sem. Mat. Fis. Univ. Milano43 (1974), 135-166. Zbl0335.18006MR352214
  19. [19] S. Mac Lane, Categories for the working mathematician, Springer, Berlin1971. Zbl0232.18001MR1712872
  20. [20] J.P. May, Simplicial objects in algebraic topology, Van Nostrand, Princeton1967. Zbl0165.26004MR222892
  21. [21] E. Michael, Local compactness and Cartesian products of quotient maps and k-spaces, Ann. Inst. Fourier (Grenoble) 18, 2 (1968), 281-286. Zbl0175.19703MR244943
  22. [22] V. Pratt, Higher dimensional automata revisited, Math. Struct. in Comp. Science10 (2000), 525-548. Zbl0956.68090MR1786473
  23. [23] D.G. Quillen, Homotopical algebra, Lecture Notes in Mathematics43, Springer, Berlin1967. Zbl0168.20903MR223432
  24. [24] G.W. Whitehead, Elements of homotopy theory, Springer, Berlin1978. Zbl0406.55001MR516508

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.