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From cubical to globular higher categories

Marco Grandis; Robert Paré

Diagrammes (2012)

  • Volume: 67-68, page 117-148
  • ISSN: 0224-3911

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Grandis, Marco, and Paré, Robert. "From cubical to globular higher categories." Diagrammes 67-68 (2012): 117-148. <http://eudml.org/doc/272980>.

@article{Grandis2012,
author = {Grandis, Marco, Paré, Robert},
journal = {Diagrammes},
keywords = {higher category; cubical category; -category; double category; bicategory; cubical set; symmetry; span; cospan; profunctor},
language = {eng},
pages = {117-148},
publisher = {Université Paris 7, Unité d'enseignement et de recherche de mathématiques},
title = {From cubical to globular higher categories},
url = {http://eudml.org/doc/272980},
volume = {67-68},
year = {2012},
}

TY - JOUR
AU - Grandis, Marco
AU - Paré, Robert
TI - From cubical to globular higher categories
JO - Diagrammes
PY - 2012
PB - Université Paris 7, Unité d'enseignement et de recherche de mathématiques
VL - 67-68
SP - 117
EP - 148
LA - eng
KW - higher category; cubical category; -category; double category; bicategory; cubical set; symmetry; span; cospan; profunctor
UR - http://eudml.org/doc/272980
ER -

References

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  2. [BH1] R. Brown and P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra21 (1981), 233-260. Zbl0468.55007
  3. [BH2] R. Brown - P.J. Higgins, , J. Pure Appl. Algebra47 (1987), 1-33. 
  4. [CL] E. Cheng - A. Lauda, Higher-dimensional categories: an illustrated guide book, draft version, revised 2004. http://www.math.uchicago.edu/~eugenia/guidebook/index.html 
  5. [CM] H.S.M. Coxeter - W.O.J. Moser, Generators and relations for discrete groups, Springer, Berlin1957. Zbl0077.02801
  6. [GPS] R. Gordon, A.J. Power, R. Street, Coherence for tricategories, Mem. Amer. Math. Soc.117 (1995), n.558. Zbl0836.18001
  7. [G1] M. Grandis, Higher cospans and weak cubical categories (Cospans in Algebraic Topology, I), Theory Appl. Categ.18 (2007), No. 12, 321-347. Zbl1127.18003
  8. [G2] M. Grandis, Collared cospans, cohomotopy and TQFT (Cospans in Algebraic Topology, II), Theory Appl. Categ.18 (2007), No. 19, 602-630. Zbl1136.18004
  9. [G3] M. Grandis, Cubical cospans and higher cobordisms (Cospans in Algebraic Topology, III), J. Homotopy Relat. Struct.3 (2008), 273-308. Zbl1185.18005
  10. [G4] M. Grandis, The role of symmetries in cubical sets and cubical categories (On weak cubical categories, I), Cah. Topol. Géom. Différ. Catég.50 (2009), 102-143. Zbl1188.18003
  11. [G5] M. Grandis, Limits in symmetric cubical categories (On weak cubical categories, II), Cah. Topol. Géom. Différ. Catég.50 (2009), 242-272. Zbl1191.18001
  12. [G6] M. Grandis, A lax symmetric cubical category associated to a directed space, in preparation. Revised version of: 'A symmetric cubical category associated to a directed space', Dip. Mat. Univ. Genova, Preprint 590 (2010). 
  13. [GM] M. Grandis - L. Mauri, Cubical sets and their site, Theory Appl. Categ.11 (2003), No.8185-211. Zbl1022.18009
  14. [GP1] M. Grandis - R. Paré, Limits in double categories, Cah. Topol. Géom. Différ. Catég.40 (1999), 162-220. Zbl0939.18007
  15. [GP2] M. Grandis - R. Paré, Adjoint for double categories, Cah. Topol. Géom. Différ. Catég.45 (2004), 193-240. Zbl1063.18002
  16. [GP3] M. Grandis - R. Paré, Kan extensions in double categories (On weak double categories, Part III), Theory Appl. Categ.20 (2008), No. 8, 152-185. Zbl1141.18006
  17. [GP4] M. Grandis - R. Paré, Lax Kan extensions for double categories (On weak double categories, Part IV), Cah. Topol. Géom. Différ. Catég.48 (2007), 163-199. Zbl1131.18004
  18. [Jo] D.L. Johnson, Topics in the theory of presentation of groups, Cambridge Univ. Press, Cambridge1980. 
  19. [K1] D.M. Kan, Abstract homotopy I, Proc. Nat. Acad. Sci. U.S.A.41 (1955), 1092-1096. Zbl0065.38601
  20. [K2] D.M. Kan, Abstract homotopy. II, Proc. Nat. Acad. Sci. U.S.A.42 (1956), 255-258. 
  21. [Le] T. Leinster, Higher operads, higher categories, Cambridge University Press, Cambridge2004. Zbl1160.18001

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