@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/item/CTGDC_2011__52_3_188_0/
[AABS02] Multiple categories: the equivalence of a globular and a cubical approach'. Adv. Math. 170 (1) (2002) 71-118. | MR | Zbl
, and '[ArMe10] The Brown-Golasinski model structure on strict -groupoids revisited'. Homology, Homotopy Appl. (2011) (to appear). | MR | Zbl
and '[Bou87] The shift functor and the comprehensive factorization for internal groupoids'. Cahiers Topologie Géom. Différentielle Catég. 28 (3) (1987) 197-226. | EuDML | Numdam | MR | Zbl
'[Bro70] Fibrations of groupoids'. J. Algebra 15 (1970) 103-132. | MR | Zbl
'[Bro99] Groupoids and crossed objects in algebraic topology'. Homology Homotopy Appl. 1 (1999) 1-78 (electronic). | EuDML | MR | Zbl
'[Bro06] Topology and Groupoids. Printed by Booksurge LLC, Charleston, S. Carolina, (2006) (third and retitled edition of book published in 1968). | MR | Zbl
[Bro08a] 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] A new higher homotopy groupoid: the fundamental globular -groupoid of a filtered space'. Homology, Homotopy Appl. 10 (1) (2008) 327-343. | MR | Zbl
'[Bro09] 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] A model structure for the homotopy theory of crossed complexes'. Cahiers Topologie Géom. Différentielle Catég. 30 (1) (1989) 61-82. | EuDML | Numdam | MR | Zbl
and '[BH81] On the algebra of cubes'. J. Pure Appl. Algebra 21 (3) (1981) 233-260. | MR | Zbl
and '[BH81a] Colimit theorems for relative homotopy groups'. J. Pure Appl. Algebra 22 (1) (1981) 11-41. | MR | Zbl
and '[BH81b] The equivalence of -groupoids and crossed complexes'. Cahiers Topologie Géom. Différentielle 22 (4) (1981) 371-386. | EuDML | Numdam | MR | Zbl
and '[BH81c] The equivalence of -groupoids and cubical T-complexes'. Cahiers Topologie Géom. Différentielle 22 (4) (1981) 349-370. | EuDML | Numdam | MR | Zbl
and '[BH87] Tensor products and homotopies for -groupoids and crossed complexes'. J. Pure Appl. Algebra 47 (1) (1987) 1-33. | MR | Zbl
and '[BH91] The classifying space of a crossed complex'. Math. Proc. Cambridge Philos. Soc. 110 (1) (1991) 95-120. | MR | Zbl
and '[BHS11] 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
, and[BM94] Covering groups of nonconnected topological groups revisited'. Math. Proc. Cambridge Philos. Soc. 115 (1) (1994) 97-110. | MR | Zbl
and '[BP96] On the Schreier theory of non-abelian extensions: generalisations and computations'. Proc. Roy. Irish Acad. Sect. A 96 (2) (1996) 213-227. | MR | Zbl
and '[BRS99] Free crossed resolutions of groups and presentations of modules of identities among relations'. LMS J. Comput. Math. 2 (1999) 28-61 (electronic). | MR | Zbl
and '[Cra99] On Combinatorial Models for Higher Dimensional Homotopies'. PhD. Thesis, Utrecht (1995). http://home. tiscali.nl/secrans/papers/comb.html
'[Dak77] Kan complexes and multiple groupoid structures. PhD. Thesis, University of Wales, Bangor (1977). http://ehres.pagesperso-orange.fr/Cahiers/dakinEM32.pdf | MR
[Day70] Construction of Biclosed Categories (PhD Thesis, University of New South Wales, 1970) http://www.math.mq.edu.au/~street/DayPhD.pdf | Zbl
[Day70a] 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] A reflection theorem for closed categories'. J. Pure Appl. Algebra 2 (1972) 1-11. | MR | Zbl
'[GM03] Cubical sets and their site'. Theory Applic. Categories 11 (2003) 185-201. | EuDML | MR | Zbl
and '[Hig71] 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] Thin elements and commutative shells in cubical -categories'. Theory Appl. Categ. 14 (2005) No. 4, 60-74 (electronic). | EuDML | MR | Zbl
'[How79] Pullback functors and crossed complexes'. Cahiers Topologie Géom. Différentielle 20 (3) (1979) 281-296. | EuDML | Numdam | MR | Zbl
'[Hue80] Crossed n-fold extensions of groups and cohomology'. Comment. Math. Helv. 55 (2) (1980) 302-313. | EuDML | MR | Zbl
'[ML71] Categories for the working mathematician, Graduate Texts in Mathematics, Volume 5. Springer-Verlag, New York (1971). | Zbl
[Pra09] The Yoneda Lemma as a foundational tool for algebra'. Stanford preprint: http://boole.stanford.edu/pub/yon.pdf (2009) 1-18.
'[Smi51] The complex of a group relative to a set of generators. I'. Ann. of Math. (2) 54 (1951) 371-402. | MR | Zbl
'[Ste06] Thin fillers in the cubical nerves of omega-categories'. Theory Appl. Categ. 16 (2006) No. 8, 144-173 (electronic). | EuDML | MR | Zbl
'[Str87] The algebra of oriented simplexes'. J. Pure Appl Algebra 49 (3) (1987) 283-335. | MR | Zbl
'[Str88] Gray's tensor product of 2-categories.' http://www.math.mq.edu.au/~street/GrayTensor.pdf (Feb, 1988). Handwritten notes.
'[SV10] The comprehensive factorization and torsors'. Theory Appl. Categ. 23 (2010) 42-75. | MR | Zbl
and '[Ton94] Theory and applications of crossed complexes. Ph.D. thesis, University of Wales (1994).
[Ton03] On the Eilenberg-Zilber theorem for crossed complexes'. J. Pure Appl. Algebra 179 (1-2) (2003) 199-220. | MR | Zbl
'[Ver08] Complicial sets characterising the simplicial nerves of strict -categories'. Mem. Amer. Math. Soc. 193 (905) (2008) xvi+184. | MR | Zbl
'[Whi49] Combinatorial homotopy. II'. Bull. Amer. Math. Soc. 55 (1949) 453-496. | MR | Zbl
'[Whi50] Simple homotopy types'. Amer. J. Math. 72 (1950) 1-57. | MR | Zbl
'