Yıl: 2000 Cilt: 49 Sayı: 1-2 Sayfa Aralığı: 39 - 48 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

The equivalence of 2-groupoids and crossed modules

Öz:
The aim of this paper is to give explicit proof of the equivalence of categories 2-groupoids and that of crossed modules, and to explore the relations of coadmissible 2-homotopy and coadmissible homotopy, respectively for 2-groupoids and crossed modules.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Diğer Erişim Türü: Erişime Açık
  • [1] R.Brown and P.J.Higgins, Crossed complexes and non-abelian extensions. In Proc.International Conference on Category Theory: Gummersbach, 1981, pp 39-50. Lecture Notes in Mathematics, Vol. 962 Springer-Verlag, 1982.
  • [2] R.Brown and P.J.Higgins, On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc. (3) 36 (1978) 193 -212.
  • [3] R.Brown and P.J.Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981) 233-260.
  • [4] R.Brown and P.J.Higgins, The equivalence of $infty$—groupoids and crossed complexes,Cahiers de Topologie et Geometrie Differentielle, Vol XXII - 4 (198-1).
  • [5] R.Brown- and P.J.Higgins, Tensor products and homotopies for $omega$-groupoids and crossed complexes. J. Pure and Appl. Algebra 47 (1987), 1-33.
  • [6] R.Brown and I.Içen, Automorphism of 2-Groupoids. In preparation.
  • [7] R.Brown and C.B.Spencer, Double groupoids and crossed modules, Cahiers Topologie-Geom. Differentielle, 17(1976) 343-362.
  • [8] R.Brown and C.B.Spencer, G-Groupoids, crossed modules and the fundemantal groupoid of a topological group, Proceeding of the Koninklijke Nederlandic Akademie van Wetenschappen, Amsterdam, Series A, valume 79(4), October 25,1976.
  • [9] A.Ehresmann and C. Ehresmann, Multiple functors. IV: Monoidal closed structure on $Cat_n$, Cahiers Topologie Geom. Differentielle, 20 (1979) 59-104.
  • [10] C.Ehresmann, Categories structurees, Ann. Sci. Ecole Norm. Sunp. (3), 80 (1963) 349-426; also in: A. C. Ehresmann, ed., Charles Ehresmann: Oeuores completes et commentees [Seven volumes] (Imprimerie Evrard, Amiens, 1984), Partie III-1.
  • [11] J.W.Gray , Formal Category Theory Adjointness for 2-categories, Lecture Notes in Math 391 (Springer -Verlag, 1974).
  • [12] İ. İçen, A version of 2-dimensional Holonomy groupoid. University of Wales, Ph.D.Thesis, 1986.
  • [13] İ. İçen and A.F.Özcan, Topolojik crossed modüller ve G-Grupoidler. XI Ulusal Matematik Sempozyumu: Isparta, 1998.
  • [14] G.M. Kelly and R. Street, Review of the elements of 2-categories, Lecture Notes in Mathematics, Vol 420 Springer, Berlin (1974) 75-103.
  • [15] C.B. Spencer, An abstract setting for homotopy pushouts and pullbacks. Caheirs Top et.Geom. Diff: XVIII -4(1977), 409-430. Springer-Verlag, 1982.
  • [16] J.H.C Whitehead, On operators in relative homotopy groups; Ann. of Math. 49 (1948)610-640.
  • [17] J.H.C Whitehead, Combinatorial homotopy II, Bull. Amer. Math. soc. 55 (1949) 453-996.
APA İÇEN İ (2000). The equivalence of 2-groupoids and crossed modules. , 39 - 48.
Chicago İÇEN İ. The equivalence of 2-groupoids and crossed modules. (2000): 39 - 48.
MLA İÇEN İ. The equivalence of 2-groupoids and crossed modules. , 2000, ss.39 - 48.
AMA İÇEN İ The equivalence of 2-groupoids and crossed modules. . 2000; 39 - 48.
Vancouver İÇEN İ The equivalence of 2-groupoids and crossed modules. . 2000; 39 - 48.
IEEE İÇEN İ "The equivalence of 2-groupoids and crossed modules." , ss.39 - 48, 2000.
ISNAD İÇEN, İ.. "The equivalence of 2-groupoids and crossed modules". (2000), 39-48.
APA İÇEN İ (2000). The equivalence of 2-groupoids and crossed modules. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 49(1-2), 39 - 48.
Chicago İÇEN İ. The equivalence of 2-groupoids and crossed modules. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 49, no.1-2 (2000): 39 - 48.
MLA İÇEN İ. The equivalence of 2-groupoids and crossed modules. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.49, no.1-2, 2000, ss.39 - 48.
AMA İÇEN İ The equivalence of 2-groupoids and crossed modules. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2000; 49(1-2): 39 - 48.
Vancouver İÇEN İ The equivalence of 2-groupoids and crossed modules. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2000; 49(1-2): 39 - 48.
IEEE İÇEN İ "The equivalence of 2-groupoids and crossed modules." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 49, ss.39 - 48, 2000.
ISNAD İÇEN, İ.. "The equivalence of 2-groupoids and crossed modules". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 49/1-2 (2000), 39-48.