Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 52 (2011) no. 3, article no. 2, 21 p.

Voir la notice de l'article provenant de la source Numdam

@article{CTGDC_2011__52_3_188_0,
     author = {Brown, Ronald and Street, Ross},
     title = {Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     eid = {2},
     pages = {188--208},
     publisher = {Andr\'ee CHARLES EHRESMANN},
     volume = {52},
     number = {3},
     year = {2011},
     mrnumber = {2866503},
     zbl = {1242.18004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CTGDC_2011__52_3_188_0/}
}
TY  - JOUR
AU  - Brown, Ronald
AU  - Street, Ross
TI  - Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product
JO  - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY  - 2011
SP  - 188
EP  - 208
VL  - 52
IS  - 3
PB  - Andrée CHARLES EHRESMANN
UR  - http://geodesic.mathdoc.fr/item/CTGDC_2011__52_3_188_0/
LA  - en
ID  - CTGDC_2011__52_3_188_0
ER  - 
%0 Journal Article
%A Brown, Ronald
%A Street, Ross
%T Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product
%J Cahiers de Topologie et Géométrie Différentielle Catégoriques
%D 2011
%P 188-208
%V 52
%N 3
%I Andrée CHARLES EHRESMANN
%U http://geodesic.mathdoc.fr/item/CTGDC_2011__52_3_188_0/
%G en
%F CTGDC_2011__52_3_188_0
Brown, Ronald; Street, Ross. Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 52 (2011) no. 3, article  no. 2, 21 p. http://geodesic.mathdoc.fr/item/CTGDC_2011__52_3_188_0/

[AABS02] Al-Agl, F. A., Brown, R. and Steiner, R. 'Multiple categories: the equivalence of a globular and a cubical approach'. Adv. Math. 170 (1) (2002) 71-118. | MR | Zbl

[ArMe10] Ara, D. and Metayer, F. 'The Brown-Golasinski model structure on strict -groupoids revisited'. Homology, Homotopy Appl. (2011) (to appear). | MR | Zbl

[Bou87] Bourn, D. 'The shift functor and the comprehensive factorization for internal groupoids'. Cahiers Topologie Géom. Différentielle Catég. 28 (3) (1987) 197-226. | MR | EuDML | Zbl | mathdoc-id

[Bro70] Brown, R. 'Fibrations of groupoids'. J. Algebra 15 (1970) 103-132. | MR | Zbl

[Bro99] Brown, R. 'Groupoids and crossed objects in algebraic topology'. Homology Homotopy Appl. 1 (1999) 1-78 (electronic). | MR | EuDML | Zbl

[Bro06] Brown, R. Topology and Groupoids. Printed by Booksurge LLC, Charleston, S. Carolina, (2006) (third and retitled edition of book published in 1968). | MR | Zbl

[Bro08a] Brown, R. 'Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups'. J. Homotopy Relat. Struct. 3 (1) (2008) 331-342. | MR | Zbl

[Bro08b] Brown, R. 'A new higher homotopy groupoid: the fundamental globular ω -groupoid of a filtered space'. Homology, Homotopy Appl. 10 (1) (2008) 327-343. | MR | Zbl

[Bro09] Brown, R. 'Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems'. In 'Michiel Hazewinkel (ed.), Handbook of Algebra', Volume 6. Elsevier (2009), 83-124. | Zbl

[BG89] Brown, R. and Golasiński, M. 'A model structure for the homotopy theory of crossed complexes'. Cahiers Topologie Géom. Différentielle Catég. 30 (1) (1989) 61-82. | MR | EuDML | Zbl | mathdoc-id

[BH81] Brown, R. and Higgins, P. J. 'On the algebra of cubes'. J. Pure Appl. Algebra 21 (3) (1981) 233-260. | MR | Zbl

[BH81a] Brown, R. and Higgins, P. J. 'Colimit theorems for relative homotopy groups'. J. Pure Appl. Algebra 22 (1) (1981) 11-41. | MR | Zbl

[BH81b] Brown, R. and Higgins, P. J. 'The equivalence of -groupoids and crossed complexes'. Cahiers Topologie Géom. Différentielle 22 (4) (1981) 371-386. | MR | EuDML | Zbl | mathdoc-id

[BH81c] Brown, R. and Higgins, P. J. 'The equivalence of ω -groupoids and cubical T-complexes'. Cahiers Topologie Géom. Différentielle 22 (4) (1981) 349-370. | MR | EuDML | Zbl | mathdoc-id

[BH87] Brown, R. and Higgins, P. J. 'Tensor products and homotopies for ω -groupoids and crossed complexes'. J. Pure Appl. Algebra 47 (1) (1987) 1-33. | MR | Zbl

[BH91] Brown, R. and Higgins, R. J. 'The classifying space of a crossed complex'. Math. Proc. Cambridge Philos. Soc. 110 (1) (1991) 95-120. | MR | Zbl

[BHS11] Brown, R., Higgins, P. J. and Sivera, R. Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids. EMS Tracts in Mathematics Vol. 15 (to appear 2011). www.bangor.ac.uk/r.brown/nonab-a-t.html. | MR | Zbl

[BM94] Brown, R. and Mucuk, O. 'Covering groups of nonconnected topological groups revisited'. Math. Proc. Cambridge Philos. Soc. 115 (1) (1994) 97-110. | MR | Zbl

[BP96] Brown, R. and Porter, T. 'On the Schreier theory of non-abelian extensions: generalisations and computations'. Proc. Roy. Irish Acad. Sect. A 96 (2) (1996) 213-227. | MR | Zbl

[BRS99] Brown, R. and Razak Salleh, A. 'Free crossed resolutions of groups and presentations of modules of identities among relations'. LMS J. Comput. Math. 2 (1999) 28-61 (electronic). | MR | Zbl

[Cra99] Crans, S. E. 'On Combinatorial Models for Higher Dimensional Homotopies'. PhD. Thesis, Utrecht (1995). http://home. tiscali.nl/secrans/papers/comb.html

[Dak77] Dakin, M. K. Kan complexes and multiple groupoid structures. PhD. Thesis, University of Wales, Bangor (1977). http://ehres.pagesperso-orange.fr/Cahiers/dakinEM32.pdf | MR

[Day70] Day, B. J. Construction of Biclosed Categories (PhD Thesis, University of New South Wales, 1970) http://www.math.mq.edu.au/~street/DayPhD.pdf | Zbl

[Day70a] Day, B. J. On closed categories of functors ; in "Reports of the Midwest Category Seminar IV", Lecture Notes in Mathematics 137 (Springer, Berlin, 1970) 1-38. | MR

[Day72] Day, B. J. 'A reflection theorem for closed categories'. J. Pure Appl. Algebra 2 (1972) 1-11. | MR | Zbl

[GM03] Grandis, M. and Mauri, L. 'Cubical sets and their site'. Theory Applic. Categories 11 (2003) 185-201. | MR | EuDML | Zbl

[Hig71] Higgins, P. J. Notes on categories and groupoids, Mathematical Studies, Volume 32. Van Nostrand Reinhold Co.; Reprints in Theory and Applications of Categories, No. 7 (2005) pp 1-195, London (1971). | MR

[Hig05] Higgins, P. J. 'Thin elements and commutative shells in cubical ω -categories'. Theory Appl. Categ. 14 (2005) No. 4, 60-74 (electronic). | MR | EuDML | Zbl

[How79] Howie, J. 'Pullback functors and crossed complexes'. Cahiers Topologie Géom. Différentielle 20 (3) (1979) 281-296. | MR | EuDML | Zbl | mathdoc-id

[Hue80] Huebschmann, J. 'Crossed n-fold extensions of groups and cohomology'. Comment. Math. Helv. 55 (2) (1980) 302-313. | MR | EuDML | Zbl

[ML71] Mac Lane, S. Categories for the working mathematician, Graduate Texts in Mathematics, Volume 5. Springer-Verlag, New York (1971). | Zbl

[Pra09] Pratt, V. 'The Yoneda Lemma as a foundational tool for algebra'. Stanford preprint: http://boole.stanford.edu/pub/yon.pdf (2009) 1-18.

[Smi51] Smith, P. A. 'The complex of a group relative to a set of generators. I'. Ann. of Math. (2) 54 (1951) 371-402. | MR | Zbl

[Ste06] Steiner, R. 'Thin fillers in the cubical nerves of omega-categories'. Theory Appl. Categ. 16 (2006) No. 8, 144-173 (electronic). | MR | EuDML | Zbl

[Str87] Street, R. 'The algebra of oriented simplexes'. J. Pure Appl Algebra 49 (3) (1987) 283-335. | MR | Zbl

[Str88] Street, R. 'Gray's tensor product of 2-categories.' http://www.math.mq.edu.au/~street/GrayTensor.pdf (Feb, 1988). Handwritten notes.

[SV10] Street, R. and Verity, D. 'The comprehensive factorization and torsors'. Theory Appl. Categ. 23 (2010) 42-75. | MR | Zbl

[Ton94] Tonks, A. Theory and applications of crossed complexes. Ph.D. thesis, University of Wales (1994).

[Ton03] Tonks, A. P. 'On the Eilenberg-Zilber theorem for crossed complexes'. J. Pure Appl. Algebra 179 (1-2) (2003) 199-220. | MR | Zbl

[Ver08] Verity, D. 'Complicial sets characterising the simplicial nerves of strict ω -categories'. Mem. Amer. Math. Soc. 193 (905) (2008) xvi+184. | MR | Zbl

[Whi49] Whitehead, J. H. C. 'Combinatorial homotopy. II'. Bull. Amer. Math. Soc. 55 (1949) 453-496. | MR | Zbl

[Whi50] Whitehead, J. H. C. 'Simple homotopy types'. Amer. J. Math. 72 (1950) 1-57. | MR | Zbl